Coventry hit the post twice in the last two minutes but Sheffield Wednesday held on for a victory that extends their winning run to five matches.
Marcus Tudgay opened the scoring after tucking away Deon Burton's neat pass.
Michael Mifsud, one of those unlucky enough to hit the post late on, equalised with a fine solo effort.
Peter Gilbert's clever pass put Chris Brunt in space and although he was foiled by Andy Marshall, Steven MacLean was on hand to lash home from 12 yards.
Sheffield Wednesday boss Brian Laws:
"It wasn't a fluent effort today.
"They got in our faces and we had to work hard, but everyone agrees it is not the performance that we're looking for at the moment - it's the result.
"I know we're getting closer. It was another win for us and it gives us another bite at the cherry."
Coventry boss Iain Dowie on his side's scoring record away from home:
"We've had six great chances to score a second. We've got the worst record of scoring away from home in the league and that tells its own story.
"We created chances at will today but if you don't score you're in trouble.
"Since I've been here it's not been too bad but we haven't solved our away from home problem and it's something I'll be looking at in the summer."
Sheff Wed: Turner, Bullen, Wood, Simek, Spurr, Whelan, Tudgay (Johnson 29), Brunt, Watson, Burton (Gilbert 64), Clarke (MacLean 46).
Subs Not Used: Adamson, Lunt.
Booked: Clarke, Wood, MacLean.
Goals: Tudgay 17, MacLean 70.
Coventry: Marshall, Hall, Page, Ward, Mifsud, Hughes, Osbourne, Tabb (Kyle 80), McNamee, Adebola, Davis (Thornton 72).
Subs Not Used: Steele, Birchall, Turner.
Booked: McNamee, Osbourne, Thornton.
Goals: Mifsud 37.
Att: 23,632
Ref: P Crossley (Kent).