Pitman smashed his effort from 12-yards out into the roof of the net to bag his 13th goal of the season.
But it was Wimbledon who had the first effort of the match after just two minutes when Cody McDonald struck his shot just wide of the Luke McGee’s post.
It was Pompey who took the lead after a lacklustre 45 minutes though when midfielder Ben Close slotted his effort into the bottom corner from outside the area.
However, five minutes into the second-half, Wimbledon drew level when striker Lyle Norris fired his penalty into the roof of the net.
The Dons then gave a penalty away themselves after referee Craig Hicks spotted a shove on Pompey captain Pitman in the 72nd minute.
The in-from striker then made no mistake in keeping his cool when he lashed his spot-kick into the top corner, sending goalkeeper George Long the wrong way.
Rangers manager Steven Gerrard is weighing up a move for Liverpool full-back Jon Flanagan, reports claim.
Scottish champions Celtic are reportedly ready to offer full-back Calvin Miller a new deal before sending him out on loan.
Everton target Jack Wilshere has sparked a scramble for his signature after confirming he is leaving Arsenal this summer.
Tottenham's hopes of landing Wilfried Zaha have been hit by the news Crystal Palace have offered him a bumper new deal to stay.
Ryan Giggs says Gareth Bale would be the perfect fit for Manchester United but has doubts over whether he will leave Real Madrid.
Manchester City's attempts to sign Riyad Mahrez could be in doubt again as reports claim Leicester only want a straight cash deal.