The teenage striker scored nine minutes after coming on, but it was the Owls centre-back who had the final word after missing two chances in the opening half.
The Sheffield side should have broken the deadlock early on in a match rearranged after the original fixture in December was abandoned with the Hillsborough turf waterlogged.
Burton O'Brien's deep corner evaded the Coventry back four and fell nicely for Wood, who pulled his far post header wide from six yards
Julian Gray exchanged passes with dangerman Michael Mifsud to lash in a low shot from a tight angle which was smothered on the line by the diving Lee Grant, before Graham Kavanagh almost found a way through with a snap-shot but the ball spun narrowly wide.
The Owls, who are in the trouble for breaking Football League rules by naming six loan signings in the squad for Saturday's match against Stoke, pressed for the opener with Ben Sahar's right-foot drive taking a deflection as the ball flashed inches wide of the target.
Coventry, who have lost three out of nine games since Chris Coleman took over last month, soaked up the Wednesday pressure and almost caught them out on the break.
Mifsud found space on the right to stroke the ball into the path of the lanky Robbie Simpson, who finished with a stinging angled shot from just inside the box which was tipped away in spectacular fashion by Grant.
Wednesday squandered another chances a minute before the break from another set-piece with Wood stretching to reach Kavanagh's corner but again heading wide from close range.
Coventry could have had a penalty in the 51st minute after Richard Duffy beat Tommy Spurr before tumbling over the full-back's outstretched leg but referee Graham Laws would have none of it.
Chances fell at both ends with Mifsud was foiled by Grant, while Johnson's fierce low drive was clutched at the foot of the post by Kasper Schmeichel.
Hines struck after Johnson's attempted clearance fell at his feet and lashed the ball past Grant, before Wood stretched to reach a long throw in to head past Schmeichel for the equaliser.