The defeat was Wednesday's first in five games after an upturn in form, but they remain six points from safety.
Story of the match
Coventry started the game the better, having 53.4% of the first-half possession in a fairly scrappy and uneventful first period.
Matty James had the game’s opening chance inside the first minute. A headed clearance from a free-kick fell at the feet of James, whose venomous strike deflected off the back of Dominic Hyam before Wednesday cleared the danger.
City then found themselves through on goal again as Julian Börner was caught out of possession, allowing Gustavo Hamer to slip Callum O'Hare through on goal. The returning Sam Hutchinson covered positionally and managed to usher the forward away from goal, forcing him to set up Ben Sheaf, who saw his effort deflect off the back of Matt Penney and stray wide.
Penney, who was making his first start since the opening day victory against Cardiff City, almost put the Owls ahead on 11 minutes. Barry Bannan opted to fizz a corner into the path of Penney, who drilled a low strike from distance towards the target, forcing Ben Wilson into an awkward save, which rolled just past his near post and wide.
On the half-hour mark, Leo Østigard came the closest to finding the opener from a corner, which came from an unforced error from Tom Lees. Østigard rose highest in the area, but his powerful header at the back post was superbly saved by former Sky Blues goalkeeper Keiren Westwood before the Owls hooked the ball clear.
The final chance of the opening period fell to Maxime Biamou, who managed to volley Sam McCallum’s deep cross high and wide of the upright.
The second half remained just as unsystematic, as the rain fell heavier in the West Midlands.
10 minutes after the restart, McCallum was played down the left, but his dangerous cross was defended well by the Owls who countered, picking out Bannan. The Scotsman instantly arrowed the ball towards the run of Josh Windass, however, his first touch was poor, and the ball rolled behind for a goal-kick.
Moments later, Coventry opened the scoring. O’Hare sharply cut in between Penney and Joey Pelupessy before threading a delightful ball through towards the edge of the Wednesday area, where Gyökeres got to the pass first to stroke the ball through the legs of Westwood.
On the hour, defender Hyam was lucky to have not seen red after wrestling Windass down to the ground as the forward raced through on goal, however, the referee only dished out a yellow card, despite being the last man.
From the free-kick, Bannan bent an effort over the wall but saw his attempt nestle on the roof of the net.
With 20 minutes remaining, Windass went close to finding an equaliser, volleying a sumptuous ball over the top from Bannan into the side-netting.
City almost confirmed their victory in the 73rd minute, forcing Westwood into a save directly from the corner before the follow-up effort was blocked on the line by Börner.
Coventry absorbed the following attacks from Wednesday, wrapping up the win in the final minute of normal time through Allen, who rolled home at the back post after a fine move from the home side.
Takeaways from the match
Coventry’s good home form continues
The Sky Blues picked up their fifth win in 12 games at St Andrew’s Stadium, earning 20 points from a possible 36.
Mark Robins must now focus on improving their record on the road, having lost eight of their 12 games, winning just twice.
Overall, City are looking on track to retain their Championship status and avoid an immediate return to League One.
Owls not creative enough
Wednesday again struggled to find a way back into the game after Coventry took the lead. Their only shot on target came in the 11th minute from Penney.
The Owls remain the Championship’s lowest scorers, finding the target 15 times in 24 games. On average, Wednesday take 8.3 shots per 90 – the lowest in the division – and of those attempts, only 2.5 of them are on target.
With several days remaining of the January transfer window, Wednesday must find a solution to their goalscoring problems if they are to avoid relegation.
Man of the match
The attacking midfielder set up both of City’s goals on Wednesday night, and was the catalyst for many of the home side’s attacks, making three successful dribbles and drawing four fouls from the Owls.
O’Hare maintained a passing accuracy of 78.6% in a virtuoso display.