The Stags came close to opening the scoring after just three minutes when James Jennings curled a free-kick fractionally wide of goal from 20 yards out.
Taylor nearly put the host in front in the seventh minute when his header from Jed Wallace's cross looped just over the crossbar.
Mansfield took the lead in style six minutes into the second half when Darryl Westlake's cross found Jennings, who set up Lee Stevenson for an exquisite overhead kick.
Chris Clements handed Ross Dyer a golden opportunity to double the lead midway through the second half but he slid his effort against the post.
Portsmouth also hit the woodwork when substitute David Connolly turned and lashed a strike against the post from 25 yards.
His arrival changed the game, though, and Taylor levelled matters when he raced on to Connolly's cross and slotted it beyond Mansfield goalkeeper Alan Marriott with 12 minutes remaining.