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.
Burton midfielder Martin Samuelsen will use the international break to recover from illness after pulling out of Norway U21's games.
Jonas Lossl is staying 'optimistic' over Huddersfield's chances of survival this season and has urged his team-mates to 'go for it'.