Sercombe struck the winner six minutes after Stuart Sinclair had cancelled out Oliver Hawkins’ opener as Rovers ended a four-match winless run.
Neither side posed much of an attacking threat in the first half.
Billy Bodin had an early shot saved for Rovers and fired wide from one of their better opportunities after 38 minutes, while at the other end Jamal Lowe had a shot deflected for a corner and goalkeeper Adam Smith denied Brett Pitman.
Portsmouth took a 64th-minute lead when Hawkins directed a header past Smith from an Adam May cross.
The visitors looked in charge until Sinclair poached an 84th-minute equaliser, pouncing to net the rebound after Pompey goalkeeper Luke McGee had failed to hold on to a Bodin effort.
And in the last minute of normal time Sercombe netted with a low shot from 25 yards through a crowded penalty area after a free-kick had been played into the midfielder’s path.
Real Sociedad have firmed up their interest in Newcastle midfielder Mikel Merino by reportedly making an opening offer of £10.5m.
Freiburg defender Caglar Soyuncu says he has turned down offers from Turkish clubs in the hope a move to Arsenal will be finalised.
Watford will reportedly listen to offers for skipper Troy Deeney but will be looking to pick up around £10million for his signature.
Huddersfield are reportedly set to join Tottenham in the race to sign Eintracht Frankfurt's Croatia international star Ante Rebic.