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.

Harvey, 21, scored five goals in 50 league appearances for the Pilgrims but rejected the offer a new contract.
Manager Gary Mills is also considering signing ex-Burton Albion striker Shaun Harrad, who has been training with the Dragons.
Harrad is a free agent after finishing the 2015-16 season at Torquay, who are keen to re-sign the 31-year-old.
"He's experienced, knows the leagues and has scored an abundance of goals in his career," Mills told BBC Wales Sport.
"I managed him at Notts County when he was a younger player so he could well be part of us as well."
Full-back Jordan Evans has also been on trial with the National League side following his release from Championship club Fulham.
Evans is a product of Wrexham's academy and Mills said the 20-year-old could sign for the club ahead of their opening league game against Dover Athletic on 6 August.

The Giants got a short-handed opener through player-coach Derrick Walser but Jeff Dimmen pulled the Panthers level.
In the second period Mike Forney's powerplay breakaway goal make it 2-1 with Andy Bohmback equalising.
Mike Radja scored from an acute angle and James Desmarais made it 4-2 before Nottingham's David Ling got one back.
The teams meet again on Saturday night in the second match of their double-header.
Nottingham lead the league on 28 points, with Sheffield Steelers on 27 and Belfast 25.
Portsmouth have secured their League Two play-off place with a victory at fellow promotion hopefuls AFC Wimbledon.
[NEXT_CONCEPT]
Wrexham have signed Plymouth Argyle forward Tyler Harvey on a one-year deal.
[NEXT_CONCEPT]
The Belfast Giants shaded a 4-3 win over Nottingham Panthers on Friday night to close the gap on the Elite League leaders to three points.