They dominated their higher-ranked opponents from the start and Gary Roberts broke the deadlock from the penalty spot.
Marc McNulty doubled the advantage before the break and arguably should have finished the tie with a hat-trick.
Ainsley Maitland-Niles reduced the deficit with a fine second half strike, although Piotr Malarczyk’s red card dented the Tractor Boys’ hopes of finding an equaliser.
Paul Cook made three changes from the side that drew 2-2 at Portman Road 10 days earlier.
Christian Burgess returned from an ankle injury to take his place in defence, meaning that Adam Barton switched to a more familiar midfield role.
There were also starts for skipper Michael Doyle and Gareth Evans, with Adam McGurk and Ben Close dropping to the bench.
Former Pompey forward Luke Varney once again led the line for Mick McCarthy’s Championship visitors.
The hosts soon took control of the tie and Kyle Bennett had an early opportunity, but could not force the ball home from a tight angle.
There was a rare opportunity at the other end on four minutes when Doyle’s header was intercepted by Brett Pitman, who sent a shot looping onto the roof of the net.
But the Blues were quickly back on the attack and Roberts hit a free-kick into the wall after Malarczyk had been booked for a foul on McNulty.
Josh Emmanuel then did well to get ahead of Evans and stop the winger from converting a dangerous cross from Ben Davies.
It was Evans who started a fine attacking move for Pompey on 30 minutes when he stole possession in the centre of the pitch.
He fed Barton, who in turn found McNulty, but Bartosz Bialkowski raced off his line to deny the striker.
The home support did not have to wait much longer to celebrate an opening goal, however.
Referee Andy Woolmer pointed to the spot when Malarczyk brought down Roberts in the box, although he opted not to show the Polish defender a second yellow card.
ROBERTS picked himself up to take the penalty and although Bialkowski got a hand to it, the keeper could not prevent the ball spinning into the net.
And the Fratton faithful were in dreamland a few minutes later, when the dominant Blues doubled their advantage.
Evans stood up a fine cross from wide on the right and McNULTY rose to head the ball home at the far post.
Ipswich Town 0
It was probably to be expected that the visitors would come out with renewed vigour after the interval.
But instead Pompey continued to play with confidence and they should have gone further ahead on 50 minutes.
Evans sent McNulty through on goal, but Bialkowski again came to Ipswich’s rescue with a fine save, while the loose ball was hooked over the line.
The Blues kept pushing forward and had another opportunity when Bennett was brought down by Josh Emmanuel just outside the box.
Roberts laid the ball off for the hovering Doyle, who hit a ferocious effort that fizzed narrowly past the post.
Pompey were also looking composed at the other end of the pitch and when Tommy Oar delivered a dangerous cross, Adam Webster calmly chested it down for Brian Murphy to collect.
But, out of nowhere, the Tractor Boys suddenly found themselves back in the tie on the hour mark.
It was a stunning 20-yard strike from on-loan Arsenal winger Maitland-Niles that flew into the top corner leaving Murphy with no chance.
Pompey immediately tried to restore their two-goal lead and Bennett was inches away from connecting with McNulty’s ball.
The chances were starting to fade as the half progressed, although Ipswich had an opening when Varney brought down a long goal-kick, only for Pitman to blaze over.
Their hopes of forcing extra-time received a blow on 77 minutes when Malarczyk brought down Roberts and was sent off for a second bookable offence.
And Pompey comfortably saw out the closing stages to book a fourth round date with the Cherries at the end of the month.
Pompey (4-2-3-1): Murphy; Davies, Burgess (Close 85), Webster, Stevens; Barton, Doyle (c); Evans, Roberts (Chaplin 82), Bennett; McNulty
Goals: Roberts 32 (pen), McNulty 37
Subs not used: Bass, May, Tollitt, Naismith, McGurk
Ipswich (4-4-2): Bialkowski; Emmanuel, Malarczyk, Digby, Kenlock; Maitland-Niles (Robinson 89), Hyam (c), Tabb (Coke 71), Oar; Varney (Toure 76), Pitman
Goals: Maitland-Niles 60
Sent off: Malarczyk (two yellow cards)
Subs not used: Gerken, Hammond, McDonnell, McLoughlin
Referee: Andy Woolmer
Attendance: 15,179 (796 away fans)