Millwall 2 Oldham Athletic 3
Having raced into an early lead, the Latics allowed their hosts back into the game and seemed to have settled for a vital away point, but Taylor had other ideas.
Deane Smalley bundled home the opener on five minutes from Neal Eardley's deep cross after a blunder from Lions' full-back Richard Duffy.
Lee Hughes doubled the visitors' lead with a glancing header from Eardley's pin-point set-piece.
The Lions were transformed after the break, having been booed off by their 8,000 strong crowd.
Record-breaking goalscorer Neil Harris got the hosts back on track from the spot after Dave Martin was fouled by Eardley. Harris drilled home confidently from the spot to make the score 2-1.
The sides were level thanks to wonder kid Ashley Grimes' magical strike 20 minutes from time. Grimes, wrapped his foot around the ball 20 yards out to curl beyond Greg Fleming to set up a tense finale.
Debutant Steve Kabba came closest to securing the points but lashed his effort over the bar from the edge of the box, but late on Taylor nodded home Smalley's cross to head home after another Duffy error.