The match appeared to be heading for a 1-1 draw as it entered extra-time, after Joe Morrell had cancelled out Rafa Ramos’ opener for the hosts.
However, in stoppage time, Harry Jewitt-White headed home from close range and then Destiny Ojo raced clear to make it 3-1 moments later in front of a 2,250 Privett Park crowd.
John Mousinho used 21 players, with only Will Norris completing the full 90 minutes, as he made nine substitutions of 64 minutes.
The late finale flattered Pompey, but here are our player ratings...
21. Christian Saydee - 7
(Replaced Callum Lang on 46 mins) Operated behind Yengi and produced his usual characteristic driving runs, going close with one second-half attempt. Produced one tremendous sliding tackle on the edge of his own area at the other end. Photo: Jason Brown
22. Kusini Yengi - 8
(Replaced Sean Patton on 46 mins) Just can't keep out of the goals. Capped second-half entrance with a lovely dink over the Gosport keeper to make it 2-0. Always in the thick of the action inside the box and picked up where the left off last season. Photo: Jason Brown
23. Sammy Silvera - 7
(Replaced Josh Murphy on 46 mins) Very bright and along with Yengi the pick of the second-half players. Went on the outside a couple of times and succeeded, on one occasion shooting into the side-netted. Supporters would have been encouraged with that display. Photo: Portsmouth FC