The Swedish striker scored twice in three minutes soon after Gustavo Hamer's opener to blow away Darren Ferguson's Posh, who remain one place outside the bottom three.
The Sky Blues, who came into the clash off the back of a 1-1 draw against Millwall last weekend, made two changes as Jamie Allen and Martyn Waghorn returned to the starting line-up in place of Ben Sheaf and Matt Godden.
The visitors opted for an unchanged line-up following their resounding 3-0 defeat of Birmingham last time out and started resolutely, teenage defender Ronnie Edwards repeatedly stifling Coventry's typically intense start as they peppered the Posh penalty area.
It was Brazilian midfielder Hamer who could have opened the scoring twice in the first half with an effort from outside the box and a free-kick he whipped over the top of David Cornell's goal, whilst Callum O'Hare would surely have scored if he got a touch to Todd Kane's cross.
Mark Robins' side, fourth before the start of play, started the second half superbly when Gyokeres twisted and turned past Dan Butler but scuffed his shot wide of the left-hand post.
The home side continued to create chances, former Brighton man Gyokeres forcing a goal line clearance from the Peterborough defence after Dom Hyam's knock-down.
Posh's resistance was finally broken after 57 minutes, though. Hamer found himself in the right place at the right time to tuck home his first goal since January after a plethora of shots on the Posh goal.
Gyokeres joined the action just after the hour mark when he was the beneficiary of another one of Kane's crosses.
Hamer started the move, shifting the ball to the right for the former Chelsea man to whip a ball into the six-yard box where Gyokeres was waiting to tap home.
The 23-year-old completed the eight-minute rout three minutes later after another mazy run inside the box, his deflected shot looping over the helpless Cornell and into the back of the net.
Peterborough's best chance came as the clock hit 90 minutes, Simon Moore thwarting Harrison Burrows with his legs as the substitute ran through on goal.
It was a thoroughly deserved win for the Sky Blues who amassed 16 shots on the way to keeping up their 100 per cent home record and keeping them flying high near the Championship summit.