Jorge Grant got Boro’ back into the game before the break, but a Nathan Thompson own goal secured all three points for the visitors in the last ten minutes.
Story of the game
Todd Kane did well down the right to squeeze the ball through to Jordan Shipley on the left of the box but his shot flew past the post for the best chance inside 10 minutes.
It was Coventry who took the lead after 15 minutes, when Hamer found himself in acres of space and unleashed a powerful drive towards goal.
Dai Cornell could only parry it into his own net as the visitors made their early dominance count.
And Coventry capitalised on the reprieve through former Posh man Matt Godden.
Kane pounced on Bali Mumba’s poor touch to slide in Godden to fire past Cornell into the far corner.
Posh did have the ball in the back of the net through Sam Szmodics but he was judged to be offside, minutes before the former Bristol City midfielder curled an effort into the hands of Wilson.
The Sky Blues should have gone further ahead when Jamie Allen was set free but his chip landed just past the post.
Peterborough took advantage of the miss by halving the deficit through Jorge Grant.
Taylor pounced on the edge of the box and it dropped kindly for Grant who curled a sublime strike into the very top corner.
Coventry finished the half the strongest, but couldn’t find a third before half time.
And Peterborough started the second half the brighter of the two, with Grant fizzing an effort wide before a sliding O’Hare hit the post at the other end.
Shipley then stung the gloves of Cornell before Hamer then curled an effort from the edge of the box agonisingly wide.
The Sky Blues were firmly on top with more corners that United eventually dealt with, before O’Hare was needlessly fouled by Josh Knight on the edge of the box, giving the visitors a great opportunity.
The short free kick to Allen almost worked but the midfielder hit the post before Godden trickled an effort into the grasp of Cornell.
Viktor Gyokeres stung the hands of Cornell as Coventry continued to search for their third as the home side failed to threaten an equaliser.
Ricky Jade-Jones looked the liveliest of any Peterborough player but he didn’t have a meaningful chance himself, but Posh had no urgency to go forward.
Coventry secured the points nine minutes from time as Kane’s cross was deflected into his own net by Thompson.
Kwame Poku fired over the bar in Posh’s first chance since the 48th minute which says all you need to know about the home side’s second half display.
In stoppage time, Godden got his second as Coventry countered with pace and the Sky Blues captain swept home into an empty net.
The Sky Blues fully deserved their win, a dominating performance from first whistle to last.
Every time they came forward they looked dangerous, while Peterborough offered very little in response.
The win moves Coventry to eighth in the league, five points outside the playoff places, while Peterborough stay 22nd, three points adrift of safety.
Cornell; Thompson, Knight, Edwards, Mumba; Taylor (Jade-Jones), Grant, Norburn; Szmodics (Poku), Dembele (Clarke-Harris), Burrows.
Wilson; Clarke-Salter, Hyam, Rose; Kane, Sheaf, Hamer (Gyokeres), Shipley (Eccles); Allen, O’Hare, Godden.