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.