The Owls looked to be heading for a second win in four days after Luke Varney's second-half striker, but up popped former Hillsborough Academy centre-half Wood – whose brother Nick is still on the Wednesday's books – to fire home a 79th-minute equaliser.
Three points for Wednesday would have gone a long way to securing their Championship status, but now it looks like an anxious end to the season.
"I don't know what to feel to be honest because I still have a lot of feelings for Sheffield Wednesday because I spent all of my career at the club up until my move here. Obviously I'm still happy that I scored the goal that got Coventry a point, but I have mixed emotions," said 24-year-old Wood. "It was strange this afternoon because I spent it kicking and tackling and challenging for headers against players I was lining up alongside at the start of the season so it took a bit of getting used to.
"I didn't want to celebrate scoring to be honest so it was bittersweet but I thought we deserved a point and I thought a draw was a fair result."
Coventry were second best in the first half and had goalkeeper Keiren Westwood to thank in the fifth minute after he pushed Darren Potter's low drive wide.
The Owls brought the best out of Westwood again when Eddie Nolan burst past Marcus Hall and shot low, but the Republic of Ireland international palmed the ball away.
In response to Wednesday's dominance, Chris Coleman made three half-time changes – and got the reaction he needed.
A 53rd-minute Clingan corner found James McPake whose header went just over the crossbar and a minute later substitute Clinton Morrison finished a Freddie Sears pass – only for it to be flagged offside.
But as Coventry pushed forward, they left holes at the back and Westwood was the hero again when he pushed a 60th-minute Leon Clarke header onto the post.
Then the Owls took the lead through Varney. The forward picked up the ball on the left wing and drifted inside the box, beating David Bell twice, before firing home from a tight angle for his ninth of the campaign. The goal could have moved the visitors away from the relegation mix, but Clingan launched a long ball in the 78th minute and Wood was on the 18-yard box to head over Lee Grant to score.
Owls boss Alan Irvine said: "It feels like two points lost, but even if we had won I'd have still said we need two wins to feel safe.
"It was a display that deserved three points. We could have done with the points but we can take the level of performance into the coming games. If we do, we'll win.
Coventry: Westwood; Cranie, McPake, Wood, Hall (Hussey 46); Baker, Clingan, Deegan, Eastwood (Morrison 46); Stead (Bell 46), Sears. Unused substitutes: Konstantopoulos, Gunnarsson, Barnett, Grandison. Booked: Hall, Cranie.
Sheffield Wednesday: Grant; Nolan, Purse, Beevers, Spurr; Soares (Gray 74), O'Connor, Potter; Varney, Tudgay, Clarke (Jeffers 82). Unused substitutes: O'Donnell, Hinds, Esajas, Simek, Boden.
Referee: Neil Swarbrick (Lancashire).
Man of the match: Keiren Westwood.
Follow all the goals go in with our Match Centre service.
This season the Yorkshire Post has an exciting new match-day service, called Match Centre. Here you will find minute-by-minute updates, stats and team formations. Plus reports from every game in England, from the Premier League down to the Blue Square Premier.
Simply select your game from the pull down menu, then click on the 'i' information button on the right of the fixture and it will give you access to everything you need to know about your team.
So if you can't make it to a game, head for the Match Centre and we will give you the best seat in the house. Click the link below.
For the latest team news, score and commentary from your team check out our new Match Centre