The visitors went ahead when Gary Roberts won possession and found Michael Smith to slide the ball home.
Wimbledon made a better start to the second half and Andy Barcham fired over, before dragging a shot wide.
Barry Fuller's goalline clearance stopped Kal Naismith from scoring Pompey's second.
Roberts also had chances in the second half but fired over the bar, before shooting wide when one on one with Kelle Roos.
Wimbledon still require two points from their last two matches to cement their spot in the play-offs.
Portsmouth have secured their League Two play-off place with a victory at fellow promotion hopefuls AFC Wimbledon.