Resurgent Sky Blues appeared to be heading for victory having recovered from Sinclair's opener after just three minutes, an exquisite finish from fully 25 yards.
Cody McDonald's header, his second goal in as many games, and Gary McSheffrey's penalty on the stroke of half-time set the Sky Blues on course to pick up three points from a losing position for the first time since September 2009.
But Posh, without an away win since Boxing Day, hit back in the 76th minute courtesy of Sinclair's second, taking his tally for the season to 10.
McDonald almost snatched victory when his late header hit a post while Sammy Clingan hit the crossbar on the full-time whistle, among four efforts to hit the woodwork in an open encounter at the Ricoh Arena.
The point sets up fourth-bottom Coventry's trip to third-bottom Bristol City on Easter Monday as a real crunch relegation clash, while Posh still have a little work to do to mathematically secure their Championship status but should be comfortable.
Out of nowhere the hosts found themselves behind within minutes of the kick-off.
Sinclair, scorer of the only goal when the two sides met at London Road in December, ran unchallenged with the ball before lofting a delicate shot over the stranded Joe Murphy and into the top corner from 25 yards.
Murphy was forced to get down well to Paul Taylor's 19th-minute strike before Lee Tomlin's delicious volley clipped the outside of a post from a well-worked short corner which followed.
The hosts were showing plenty of endeavour but lacking any kind of composure in the final third.
But all that changed in the 26th minute.
Oliver Norwood's cross-field pass was brought down by Jordan Clarke at the far post and he lofted an inviting cross for McDonald to head past Paul Jones.
The encounter flowed from end-to-end as both sides looked to create an opening, albeit without success, and it was left for a mistake to lead to Coventry's second on the stroke of half-time.
Tomlin upended the impressive Clarke in the area and McSheffrey stepped forward to send Jones the wrong way from the spot.
An even livelier start to the second period followed as Taylor and Sinclair wasted openings while McSheffrey and Alex Nimely brought solid saves from Jones at the other end.
Amid all that Gabriel Zakuani was fortunate to see his clearance clip the outside of a post as he looked to clear McSheffrey's dangerous cross.
But it was left for Sinclair to rescue a share of the spoils for Peterborough with 14 minutes remaining, poking home skipper Grant McCann's corner from close range.
McDonald almost snatched victory for Coventry but he could only watch as his header rebounded back of the woodwork, with Clingan then striking the bar after Posh had seen penalty appeals turned down at the other end.