The Blues progressed to the second round of the competition following Sean Raggett’s controversial winner for the visitors in extra-time.
The centre-back looked in an offside position when he tapped the ball across the line on 111 minutes.
Pompey raced into a 2-0 lead through goals from Ronan Curtis (11 minutes) and Tom Naylor (13).
The Tractor Boys fought back through Jon Nolan (43) and James Norwood (66) – but it’s Pompey who are in the hat for the next round thanks to Raggett’s intervention.
13. Haji Mnoga - 6
(replaced Callum Johnson on 50 minutes): Put himself about and could have scored at the death. Photo: JPIMedia
14. Ellis Harrison - 6
(replaced Ronan Curtis on 74 minutes): Burly presence and made nuisance of himself. Photo: JPIMedia
15. Bryn Morris - 6
(replaced John Marquis on 90 minutes): Was played out of position but was quietly effective. Photo: JPIMedia