Christian Burgess marked his 200th appearance with a goal, as Pompey won the battle of two in-form teams at Fratton Park.
It was Ronan Curtis who assisted his first half header, before then teeing-up James Bolton to secure all three points the break.
From the moment they took the lead, it was a dominant display from the Blues against their promotion rivals.
The Black Cats received a further blow late on when, having made the maximum number of substitutions, Joel Lynch was stretchered off the pitch.
Kenny Jackett made one change from the side that won at Lincoln earlier in the week to complete an unbeaten January.
On-loan Barnsley midfielder Cameron McGeehan returned to the starting line-up, with Ben Close dropping to the bench.
The visitors made the faster start to the contest and Charlie Wyke did well to get a shot away after latching onto a ball down the left.
But Bass was able to keep out his effort and the keeper then leapt on the loose ball to deny a follow-up opportunity.
Pompey soon had a chance of their own at the other end, with Ryan Williams glancing a fine Curtis free-kick agonisingly past the post.
Again the action switched in what was proving to be an engrossing half of football and Hume cut the ball back for an unmarked Chris Maguire.
It looked as though the former Fratton loanee would score against his former club, only to screw his shot horribly, allowing Burgess to head clear.
The visitors were again left wondering how they had not taken the lead when Luke O’Nien’s fine effort hit the post and then ricocheted off the back of Bass before bouncing narrowly wide.
Instead it was Pompey who broke the deadlock on 25 minutes after Curtis had been fouled wide on the left.
He sent a superb delivery into the box and BURGESS was there to nod home and score for a third successive Saturday.
The lead was almost doubled a few minutes later when the ball bounced into John Marquis’ path and he hit a fierce effort just off target.
Steve Seddon’s set-piece was then headed back by Sean Raggett in a crowded box, but it was a Sunderland boot who got there first.
The Blues had been totally on top since taking the lead and they had two more great chances to score again in quick succession before the break.
First, Jon McLaughlin made a superb save when Curtis’ delivery took a wicked deflection off Bailey Wright and headed towards the net.
Andy Cannon then cut the ball back for Bolton, who miscued his close-range shot and saw the ball fly wide.
Tempers threatened to boil over in the final seconds of the first half after Bass beat Wyke to the ball and the striker tumbled over him.
The Black Cats wanted a penalty and referee Christopher Sarginson rightly waved away their appeals.
It led to an argument near the touchline and, when things settled down, both Lynden Gooch and Seddon were booked.
Jackett made a change at the start of the second half, with Ellis Harrison taking over from Marquis up front.
But it was Williams who soon had a chance to score a second for the Blues, meeting Bolton’s cross with a header that flew narrowly wide.
Instead it was another member of the back four who gave the hosts a welcome cushion on 52 minutes.
Curtis was the provider once more, whipping in a fine corner that BOLTON bundled home from a few yards out.
Pompey were threatening to run riot and when Curtis’ cross was nodded back by Williams, a Harrison header was kept out by McLaughlin from point-blank range.
Cannon’s follow-up attempt was blocked and the midfielder then teed-up Raggett, who fired wastefully past the post.
The Fratton faithful were enjoying themselves and jeered George Dobson when the midfielder swiped at thin air and conceded a throw.
It was pretty much one-way traffic, as the Blues continued to play with a real swagger, while their opponents offered little going forward.
And whenever the hosts did lose the ball, they were quickly gifted possession straight back again by the below-par Black Cats.
McLaughlin had to come out of his box to stop Harrison reaching Bolton’s clearance on 81 minutes and recovered to stop Williams following up.
He unfortunately collided with Lynch in the process, though, and the defender received lengthy treatment on the pitch before being stretchered off.
All four sides of Fratton Park rose to applaud the stricken player, but Sunderland had already made all three changes and had to finish the game with 10 men.
It meant there were nine minutes of injury-time for Pompey to negotiate, but they looked more likely to add to the scoring.
McLaughlin made another fine save to keep out Harrison’s swerving shot, as the Blues comfortably saw the contest out.
Pompey (4-2-3-1): Bass; Bolton, Burgess, Raggett, Seddon; Naylor (c), McGeehan; Williams, Cannon (Close 90+5), Curtis; Marquis (Harrison 46)
Goals: Burgess 25, Bolton 52
Booked: Seddon, Raggett
Subs not used: MacGillivray, Whatmough, Brown, McCrorie, Harness
Sunderland (3-4-3): J.McLaughlin; Willis, Wright, Lynch; O’Nien, Dobson, Power (c), Hume (Semenyo 69); Maguire (Watmore 69), Wyke (Lafferty 46), Gooch
Booked: Gooch, Dobson, Semenyo
Subs not used: Burge, C.McLaughlin, Flanagan, Scowen
Referee: Christopher Sarginson
Attendance: 18,531 (1,819 away fans)
FA Cup 3
Goals from James Bolton and John Marquis ensured Pompey won at Fleetwood to reach the fourth round of the Emirates FA Cup for a second successive season.
There was little to separate the League One promotion hopefuls before the break at a chilly Highbury Stadium.
But the visitors were more clinical in a rain-soaked second half and James Bolton arrived at the far post to open his Blues account.
John Marquis added a second in similar fashion soon after and Conor McAleny’s stoppage-time effort proved no more than a consolation.
Kenny Jackett made three changes from the side that collected a point at Gillingham on New Year’s Day.
Loan signing Steve Seddon went straight into the starting line-up following his arrival from Birmingham on Thursday.
There were also returns for both Marquis and Andy Cannon, with Gareth Evans, Ben Close and Ellis Harrison dropping to the bench.
With Seddon slotting in at left-back, the versatile Anton Walkes moved up to join skipper Tom Naylor in the midfield engine room.
The game – as with all third round fixtures – began one minute late to give everyone the chance to think about looking after their mental health.
There was an early chance for the visitors once the action started, with Bolton looping a header narrowly wide following good work down the left by Marcus Harness.
Marquis then cried for a penalty after going down in a challenge for the ball with Ashley Eastham, although referee Marc Edwards ignored his appeals.
It was generally a slow opening to the contest, however, with neither keeper being called into action.
There were fears for Wes Burns when a clearance from Seddon smacked into his head from point-blank range, but the winger was quickly back on his feet.
On a cold evening on the Fylde coast, there were only half-chances to excite the travelling fans, with a fierce volley from Cannon fizzing not too far off target.
But the action intensified as time progressed and a passage of patient passing play from Pompey ended with the lively Harness drawing a save from Alex Cairns.
Paddy Madden’s effort was then comfortably stopped by Alex Bass at the other end, while an attempt from Marquis was blocked by Harry Souttar.
The quick feet of Harness were causing problems for the hosts and after racing across the six-yard box, he could only find the side netting.
Fleetwood were seeing plenty of the ball, but not really testing Bass, although a Josh Morris free-kick was diverted narrowly over his own bar by Marquis.
The visitors won a set-piece themselves before the break and Seddon’s delivery was nodded off target by Sean Raggett.
Fleetwood Town 0
The rain was falling when the sides returned after the break, but clear-cut openings continued to be at a premium.
Bass dealt with a dangerous Burns cross, while Christian Burgess’ block denied Cod Army left-back Danny Andrew.
It then took a perfectly-timed challenge in the box from Harry Souttar to stop Cannon from Converting Marquis’ threaded pass.
The contest was lacking quality in the final third, although a delivery from the impressive Harness caused problems as it bounced around the box before being hacked clear.
And another cross – this time from Curtis – led to the Blues finally breaking the deadlock on 66 minutes.
Fleetwood failed to deal with the danger and the ball appeared to get flicked on inside a packed box before BOLTON bundled it over the line from a yard out.
There probably should have been an immediate leveller, but an unmarked Madden scooped high over the bar from Burns’ cut-back.
Pompey quickly made them pay, as Seddon’s corner was headed powerfully back across goal by Burgess and MARQUIS converted at the back post.
The hosts were trying to find a route back into the tie, but some more wasteful finishing from Madden was proving costly.
Seddon was replaced by Close – making his 150th Blues appearance – late on, as Jackett introduced some fresh legs.
Fleetwood were given hope in stoppage-time, as a strike from substitute McAleny took a deflection to beat Bass.
That caused hearts to flutter in the away end of Highbury, but the Blues saw out the closing stages to secure their progress.
Fleetwood (4-4-2): Cairns; Coyle, Eastham (McAleny 83), Souttar, Andrew; Burns, Coutts (c) (Sowerby 72), Dempsey, Morris; Madden (Saunders 81), Evans
Goals: McAleny 90+1
Subs not used: Gilks, Hill, Biggins, Garner
Pompey (4-2-3-1): Bass; Bolton, Burgess, Raggett, Seddon (Close 81); Naylor (c), Walkes; Harness, Cannon, Curtis; Marquis
Goals: Bolton 66, Marquis 72
Booked: Raggett, Walkes
Subs not used: MacGillivray, Downing, Evans, Hawkins, Pitman, Harrison
Referee: Marc Edwards
Attendance: 2,145 (525 Pompey fans)