The two sides kicked off separated only by goal difference and Posh needed just eight minutes to hit the front as Reece Brown finished coolly after City keeper Matt Ingram parried a Sammie Szmodics cross-shot into his path.
But the Tigers levelled when Reece Burke rose to head in a George Honeyman free-kick in the 21st minute and they were handed a numerical advantage when Posh midfielder Ethan Hamilton was dismissed five minutes before the break after a late lunge on Lewie Coyle earned his second caution.
Despite being reduced to 10 men, Posh were agonisingly close to restoring their advantage in the dying seconds of the first half when a Joe Ward free-kick bounced against a post.
But predictably it was Hull who made the extra man count to forge ahead four minutes into the second half when Keane Lewis-Potter fired in Callum Elder’s cross from the left.
The result was put beyond doubt in the 59th minute when Malik Wilks tucked away his 20th goal of the season from the penalty spot after Honeyman was brought down by Frankie Kent.
Hull manager Grant McCann refused to get carried away.
McCann, a promotion-winning Posh player and former club boss, said: “It was a good performance and a good result.
“Peterborough are the best team in the league at home. Not many teams come here, go a goal down and come back to win so I’m very proud.
“Peterborough started very strongly whereas we started slowly, but we stayed calm and got ourselves level.
“The red card was clear. Lewie is in the dressing room strapped up and was lucky not to have his leg broken by the challenge.
“Some might say the sending-off was a pivotal moment, but personally I feel we would have won the game 11 v 11 anyway.
“This win is no more significant than the last one to be honest, though.
“If we had lost I would probably have been asked if it was our automatic promotion hopes gone. That’s how quickly things change. There are still a lot of games left and lot of twists and turns ahead.”
Posh boss Darren Ferguson admitted: “We were outstanding for the first 20 minutes and I couldn’t believe how much we were in control.
“We caused them all kinds of problems from minute one and could have been three up but then conceded a terrible goal from a set-piece.
“I thought Ethan’s first booking was soft as it was his first tackle in the game, but once cautioned you have to stay on your feet.
“Watching the second challenge live I actually thought it was Ethan fouled, but having seen it back it is a yellow card.
“I told the lads at half-time that we were still very much in the game but we conceded two more dreadful goals.
“Rather than focusing on the red card, we have to look at the manner of the goals we gave away. That hasn’t been good enough of late and the opposition haven’t had to work for it.”