Middlesbrough shaded a dull opening period, and were rewarded early in the second half when Matthew Bates' header deservedly put them ahead.
But Posh rallied and won a point when Taylor curled home a glorious shot into the top corner with only 10 minutes remaining.
Both sides went for the winner in a pulsating finale but had to settle for a point apiece.
The game was a match-up between the Championship's leakiest and meanest defences, and Middlesbrough - who have conceded only 14 League goals this season - were rarely tested early on by an ineffective Peterborough attack.
The visitors, however, were restricted to long-range efforts, but came close through Tony McMahon's free-kick which whistled narrowly wide from 20 yards after 32 minutes.
Although Boro were dominating the early stages, Peterborough improved as the half wore on and a rampaging run down the right from Tommy Rowe found Lee Tomlin, whose shot was blocked by Stephen McManus.
From that move, Middlesbrough broke on a counter-attack which ended with Barry Robson's strike from 25 yards, which had Paul Jones scrambling, but was just wide of the post.
The Posh have failed to keep a clean sheet whilst already conceding 30 Championship goals this season, but as half-time approached, Darren Ferguson's thoughts must surely have been turning to that being a possibility.
Peterborough have not been involved in a goalless draw since December 2009 but that notion, and that of a clean sheet, was quickly dismissed seven minutes after the interval.
A McMahon corner was met by Bates, who had waltzed into the box unmarked and seemingly unnoticed to power a header into the top corner for his first goal of the season.
And it took 64 minutes for the hosts to finally test Jason Steele when George Boyd broke clear but the England under-21 keeper did well to spread himself and keep Boyd's effort out with his feet.
Boro were still looking dangerous going forward, but Peterborough were becoming more adventurous and were unlucky not to level in the 79th minute when Tom Kennedy's blistering run and shot from 20 yards smashed against a post.
But the equaliser came two minutes later when the ball ricocheted to Taylor, who curled a superb effort past the outstretched dive of Steele and into the top corner.
Both sides were pushing for the points and free-kicks from Grant McCann and Tony McMahon failed to beat either goalkeeper, while Middlesbrough midfielder Faris Haroun appeared to have raised his hand to referee Stuart Attwell and may face retrospective action.