Cyrus Christie launched a desperate cross to the far post in time added on and, after Leeds goalkeeper Paul Rachubka could only parry the ball, Wood pounced to cancel out Darren O'Dea's first-half opener.
It was just reward for the visitors, who refused to buckle under long periods of pressure, and Leeds were made to pay for a hatful of missed chances in either half.
Republic of Ireland international defender O'Dea drove home an angled shot midway through the first half, but the home fans were left to endure an anxious finish and watched in despair as Wood made Simon Grayson's side pay.
Leeds' 10-goal leading goalscorer Ross McCormack miscued from six yards with only Coventry goalkeeper Joe Murphy to beat just before half-time.
And Leeds midfield pair Danny Pugh and Adam Clayton were both denied by an inspired Murphy in the second period.
Coventry were always in the hunt and had Lukas Jutkiewicz kept his flying late header a shade lower in the closing stages, the Sky Blues would have been level earlier.
Rachubka made his first league start for the club in place of Andy Lonergan, who injured a finger in last Friday's 3-0 win at Doncaster.
Coventry manager Andy Thorn named the same side that started in their 1-0 home win over Nottingham Forest on Saturday.
The home side almost took a sixth-minute lead when Robert Snodgrass curled a fine cross with the outside of his boot into the penalty area and McCormack stole in between the visitors' central defenders to head inches over the crossbar.
But Coventry launched an early riposte as skipper Sammy Clingan's 25-yard shot forced Rachubka to parry at full stretch and Jutkiewicz blasted the rebound narrowly off target.
Murphy was then at full stretch to keep out Snodgrass' clipped free-kick as Leeds began to press for the opener, which duly arrived courtesy of an unlikely outlet in the 26th minute.
Paul Connolly's cross was deflected to the left side of the penalty area and centre-half O'Dea arrowed a striker's finish, left-footed, into Murphy's bottom left-hand corner.
Murphy did well to keep out McCormack's stinging drive and the Scottish striker spurned a gilt-edged chance in the 41st minute when lifting the ball over the crossbar following excellent work by Andy Keogh.
Coventry showed more urgency after the break, no doubt buoyed by Leeds' missed first-half chances, but the home side stepped up a gear around the hour mark and went close to extending their lead on three occasions.
Pugh's bullet header was superbly saved by Murphy and after Snodgrass' raking drive whistled past the post, the visiting goalkeeper was at his best again to keep out Clayton's low shot from inside the area.
Leeds favourite Luciano Becchio and Mikael Forssell replaced Keogh and McCormack in the 70th minute as boss Grayson chased that elusive second goal.
Coventry striker Jutkiewicz almost equalised for the visitors with a fine header as Leeds grew increasingly nervous in the closing stages, before defender Wood latched onto Rachubka's fumble to stab the ball home at the far post.