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...
9. Callum Lang - 7
(Replaced by Christian Saydee on 46 mins) Along with Murphy, Pompey’s chief attacking threat in the first half and posed plenty of problems with his energy and enthusiasm. Claimed an assist too for Josh Murphy's goal. Photo: Jason Brown
10. Josh Murphy - 8
(Replaced by Sammy Silvera on 46 mins) A mercurial performance from the left winger, who took just 20 minutes to open his Pompey goal account with a right-footed finish from Callum Lang's pass. A constant threat, gliding across the ground and often showing blistering pace. Very, very encouraging. Photo: Portsmouth FC
11. Triallist B (Sean Patton) - 5
(Replaced by Kusini Yengi on 46 mins) The youngster wasted a couple of glorious opportunities, hitting both over the bar first time when well placed. Certainly not the first introduction to the fans he would have wanted in a disappointing showing. Photo: Jason Brown
12. Gosport Borough hosted Portsmouth FC in their opening pre season friendly at Privett Park on Tuesday night. Pictured - General Action Photos by Alex Shute
Marlon Pack in action for Pompey against Gosport. Picture: Alex Shute Photo: Alex Shute