George Hirst had provided an early lead, but the afternoon threatened to unravel when Marcus Harness was dismissed midway through the first half.
Instead, however, the Blues merely stepped up their performance and Sean Raggett’s header gave them a healthy advantage at the break.
Stanley tried their best to battle back, but further goals from Hirst and the impressive Ryan Tunnicliffe wrapped up a comfortable victory.
Danny Cowley made two changes from the side that fought from behind to beat Oxford on home soil earlier in the week.
Tunnicliffe and skipper Clark Robertson both returned to the starting line-up, as Joe Morrell and Denver Hume dropped to the bench.
The visitors almost enjoyed a perfect start, as a long-range effort from Josh Woods dipped narrowly over the crossbar.
A corner routine then saw Tunnicliffe send in a fine delivery, but Accrington had too many bodies back for a shot to get through to test Toby Savin.
But the breakthrough did arrive for the Blues on 16 minutes after a quick counter from a Stanley corner.
Mahlon Romeo combined well with Harness on the right and cut the ball back for HIRST to divert into the bottom corner.
It quickly went from ecstasy to agony for the Fratton faithful, though, as they were reduced to 10 men.
Harness made a reckless two-footed challenge from behind on Ross Sykes and referee Carl Brook immediately reached for his back pocket to show a red card.
Pompey were still looking to attack despite that setback and it took a fine sliding challenge from Michael Nottingham to prevent Hirst getting a shot away.
But a second goal did arrive from the resulting corner, as RAGGETT rose above Sykes to emphatically convert a Tunnicliffe cross.
Accrington tried their best to get back into the contest, but the hosts were defending resolutely, with one fine interception from Hayden Carter drawing warm applause.
There were a couple of nervy moments late in the half, however, and Gavin Bazunu twice had to come to the rescue.
He got down quickly to deal with a low Woods drive and then made an even better stop to deny Rosaire Longelo, who had been left in far too much space from a corner.
Accrington Stanley 0
The home side were fuming soon after the restart, when Harry Pell – who had been brought off the bench – scythed down Louis Thompson.
He was only shown a yellow card for the challenge, with Pompey players understandably pointing out the official’s earlier punishment for Harness.
The boos turned to cheers on 56 minutes, though, as the hosts extended their advantage even further.
It was similar to the second goal, with HIRST this time the man to barge past Sykes and emphatically convert a Tunnicliffe corner.
Pompey’s set-pieces were causing plenty of problems and another Tunnicliffe flag-kick was unconvincingly palmed away by Savin.
Accrington were trying to cause threats of their own and Pell’s looping header had to be tipped over by Bazunu.
They went even closer from the resulting corner, as Sykes’ effort was blocked and the ball pinged around the box before being fired wide.
But, incredibly, it was the Blues who scored again on 69 minutes and it was all down to some great play from Aiden O’Brien.
He picked up the ball inside his own half and ran up the pitch, bursting between Sykes and Ethan Hamilton before cutting back for TUNNICLIFFE to fire home.
Cowley used his bench to bring some fresh legs on, as Thompson and Hirst made way for Morrell and Tyler Walker.
And there was even time for Jay Mingi to come on for his debut in place of O’Brien, who has already become a fans’ favourite on the south coast.
Accrington saw plenty of the ball during the closing stages, but the Blues remained resolute to add a clean sheet to their three points.
Pompey (3-4-1-2): Bazunu; Carter, Raggett, Robertson (c); Romeo, Tunnicliffe, Thompson (Morrell 72), Ogilvie; Harness; O’Brien (Mingi 78), Hirst (Walker 73)
Goals: Hirst 16, 56, Raggett 28, Tunnicliffe 69
Sent off: Harness
Booked: Robertson, Romeo
Subs not used: Webber, Vincent, Hume, Jewitt-White
Accrington (3-4-1-2): Savin; Sykes, Nottingham, Amankwah (Longelo 34); Rodgers (Leigh 52), Conneely (c) (Pell 46), Butcher, McConville; Hamilton; Woods, Bishop
Booked: Pell, Nottingham
Subs not used: Isherwood, Rich-Baghuelou, Morgan, Adedoyin
Referee: Carl Brook
Attendance: 15,091 (144 away fans)