The 23-year-old striker, making only his fourth appearance since joining from Anderlecht last season, crashed in an equaliser from 25 yards as Posh came back from the dead at The Den.
Millwall were 2-0 up and cruising when, early in the second half, Hameur Bouazza struck to add to Liam Trotter's first-half opener.
But Lee Frecklington pulled one back and, moments after Millwall rattled the woodwork Taylor, who was once hit with a six-month FA drugs ban while playing for Chester, salvaged a draw.
It was a deserved point for newly-promoted Posh, who lasted just one season the last time they came up.
They are easy on the eye when attacking but will need to improve dramatically at the back if they are secure a longer stay this time.
George Boyd remains their most dangerous player and he was a lick of paint from opening the scoring in the 17th minute.
Lions goalkeeper David Forde came for, and completely missed, Grant McCann's cross and Boyd's angled volley bounced into the ground and back off the post.
But Millwall still looked the more threatening, with Posh keeper Paul Jones pulling off fine saves from James Henry, Darius Henderson and Bouazza.
But he could do nothing to prevent the opening goal in the 32nd minute, and it was all too easy for the hosts.
Henry raced down the left and played the ball inside to Henderson who, totally unchallenged, took a couple of touches inside the area before squaring for Trotter to sidefoot home from 10 yards.
Trotter almost grabbed a spectacular second in first-half stoppage time but his volley was clawed away by Jones.
Millwall doubled their lead in the 55th minute thanks to another slick move and some non-existent marking.
Bouazza was in too much space in the area when Henderson played him in and the winger took just one touch before blasting the ball across Jones and into the corner.
But Posh pulled one back in the 72nd minute when Taylor set up Frecklington to drive home from the edge of the box.
Trotter then smashed a shot against the post as Millwall looked to restore their advantage.
But instead, in the 75th minute, Taylor stole possession midway inside the Lions' half, strode forward and thumped a low shot past Forde and into the corner.