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.
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