Substitute Steve MacLean struck in the 70th minute to keep alive Wednesday's slim hopes of a play-off spot and improve his chances of earning a new contract.
The 24-year-old striker, whose present deal runs out in the summer, extended the Hillsborough side's unbeaten run to 11 games after Coventry had cancelled out Marcus Tudgay's early strike.
Tudgay linked cleverly with Leon Clarke early in the game but the big striker finished tamely before the Owls snatched the lead in the 17th minute, Deon Burton squaring the ball to Tudgay who stroked it beyond Andy Marshall's reach from 14 yards.
On-loan keeper Iain Turner, playing his last game before returning to Goodison Park, misjudged a Stephen Hughes free-kick and was at fault again when he was beaten to a Hughes corner by the alert Elliott Ward whose downward header flashed over the woodwork.
Wednesday escaped again on 23 minutes as Coventry, chasing their first win in five games, stepped up the pace. Full-back Frank Simek cleared Dele Adebola's close-range strike off the line as Iain Dowie's side pressed again.
Substitute Jermaine Johnson, on for the injured Tudgay, made an instant impact cutting inside from the right flank before lashing in a fierce cross. The ball deflected off Ward and flashed a fraction wide of the far post.
Coventry were back on level terms in the 37th minute from a move started and finished in spectacular fashion by Malta international Michael Mifsud. The little striker turned past defenders Tommy Spurr and Richard Wood before slamming the ball into the top right-hand corner from ten yards out.
Chris Brunt almost blasted Wednesday into the lead minutes before the interval, Marshall producing a spectacular one-handed stop to push away his stinging 25-yard free-kick.
Adebola blundered on the hour as he climbed unmarked to meet a cross from midfielder Jay Tabb and casually headed the ball wide from five yards.
MacLean had the last word lashing the ball past the stranded Marshall with 20 minutes left after the Coventry keeper had pushed away a Brunt shot, although the lively Mifsud was denied by the woodwork in the dying minutes, his low strike crashing against the foot of the post.