City prop up the second tier going into Christmas Day, already eight points from safety, with only one team in the past 12 seasons having avoided the drop when in the same position.
Saturday’s result at London Road was harsh on Andy Thorn’s side, who struck a post in the 87th minute through Gary Gardner, saw Gabriel Zakuani clear off the line in injury time, went close on a couple of occasions with Lukas Jutkiewicz and Chris Hussey and had loud appeals for a penalty waved away after Craig Alcock appeared to handle in the area.
But it was Posh, who improved after a below-par first-half display, who registered the only goal of the game in the 66th minute – game-changing substitute Paul Taylor teeing up Emile Sinclair for his sixth of the season for the club.
It was far from free-scoring Peterborough, who clinched their first clean sheet of the season, but it was enough to leave the unfortunate Sky Blues still searching for their first away win of the campaign.
Both sides went into the game desperately needing all three points, with Posh having won just one of their last nine and Coventry losing six of their last seven.
Coventry were getting plenty of numbers behind the ball and making life difficult for their hosts, who were struggling to get going.
Gardner’s set-piece forced a solid save from Joe Lewis before Jutkiewicz headed over from close range, sandwiching a Lee Tomlin effort from 20 yards which forced Joe Murphy into routine action.
Tomlin was by far and away Posh’s most dangerous player and his shot on the turn, which sailed just over the crossbar, was the closest the home side went in the opening 35 minutes.
And as the half-time whistle blew it was Sky Blues boss Thorn who would have been the happier of the two managers.
Counterpart Darren Ferguson waited just four second-half minutes before making a change, Taylor replacing Lee Frecklington.
And Taylor almost made an immediate impact as he set up Daniel Kearns, making his full debut, but Murphy saved well with his feet.
Taylor’s introduction seemed to spark life into Peterborough and skipper George Boyd was next to go close.
Jutkiewicz reminded United of the visitors’ threat with a shot from distance which was turned around by Lewis, with Coventry seeing solid penalty claims for handball against Alcock dismissed from the resulting corner.
It was an end-to-end affair as both sides went in search of a breakthrough, Taylor going close for the home side before Jutkiewicz and Hussey did the same for City.
And it was Peterborough who got the vital breakthrough thanks to lively substitute Taylor, who saw his initial attempt saved by Murphy before pulling the rebound back for Sinclair to fire home.
Murphy raced off his line to save well from Sinclair but it was Coventry who threatened an equaliser in the closing stages.
Clive Platt and Cyrus Christie went close, as did Gary McSheffrey, although it was Gardner who almost snatched a point when his strike rebounded off a post.
But it was not to be as Jutkiewicz saw his 94th-minute effort cleared off the line by Zakuani.