The Dons had calls for a penalty waved away after only two minutes when Danny Hylton appeared to be tripped in the Portsmouth box. Referee Stuart Attwell adjudged the foul to have taken place outside of the penalty area, though, and instead awarded the visitors a free-kick.
Charlie Wyke should have put Wimbledon in front after four minutes but struck wide of the far post.
Despite lacking any serious attacking threat in the opening 45 minutes, Pompey took charge when Taylor bravely met Daniel Alfei's cross from the right with a looping header seven minutes after the break.
However, Taylor clashed heads when he won the ball and was replaced by Patrick Agyemang just before the hour mark.
Pompey keeper Trevor Carson denied the visitors a leveller as he stopped Alan Bennett's header from George Francomb's free-kick at point-blank range.
Neal Ardley's side forced Portsmouth to defend frantically in stoppage time and a Luke Moore strike was cleared off the line, yet the hosts held on for a huge three points.