The Blues won the game 3-1, with all the goals coming in the first half.
Joe Pigott handed the hosts the lead on 23 minutes in controversial circumstances.
But Pompey responded a minute later through Ronan Curtis, before two late first-half strikes from Lee Brown secured the win that keeps the Blues sixth in the table and in control of their own play-off destiny after Charlton could only draw at Accrington.
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5. AFC Wimbledon v Pompey
Ronan Curtis sees his 24th-minute effort find the back of the net. Photo: Jason Brown
8. AFC Wimbledon v Pompey
John Marquis looks to set up a Pompey attack. Photo: Jason Brown