Neill Collins emerged as what his manager called "an unlikely hero" with the late goal that earned Wolves a victory that could revitalise their season.
A tense, untidy game was wandering towards what seemed the inevitability of a goalless draw when Coventry, marginally the better side for most of the afternoon, gave away a needless corner.
They could then only clear it back to Michael Kightly on the byline and the game's most creative player put it back in for the substitute defender to head emphatically passed Andy Marshall in the third minute of time added on.
"He attacked it brilliantly and we managed the only bit of magic of the game", said Mick McCarthy as he savoured the late strike that lifted his side above City in the upper reaches of the Championship table. "Maybe we had that bit of good fortune that we've not had in the last two games."
Collins was only on the field because of the misfortune that befell Wolves' experienced left-back Michael Gray in the first half. Gray tore a hamstring in a 50-50 tackle and Wolves also lost their goalkeeper, Wayne Hennessey, after a collision with Robbie Simpson saw him taken to hospital for X-rays.
That disruption, plus the understandable confidence of a Coventry side with a win at Old Trafford on their recent CV, made it look like an increasingly difficult afternoon for Wolves.
Wolves' lack of punch cried out for their leading scorer, Freddy Eastwood, who was duly brought on only to show, with his lack of touch, why he was not in the starting line-up.
Coventry, with "The Mosquito" – Michael Mifsud, whose goals beat Manchester United – buzzing angrily, looked the more likely winners and probably would have been if their captain, Michael Doyle, had converted a glorious chance when sent through by Jay Tabb, rather than steering it beyond the far post.
That left the door ajar for Collins and Woods. "It wasn't a game we deserved nothing out of," said the Coventry manager, Ian Dowie. "But that's football."
Goal: Collins (90) 1-0.
Wolves (4-4-2): Hennessey (Stack, 30); Foley, Breen, Craddock, Gray (Collins, 20); S Ward (Eastwood, h-t), Olofinjana, Henry, Kightly; Keogh, Elliott. Substitutes not used: Bothroyd, Gleeson.
Coventry City (4-4-2): Marshall; Osbourne, E Ward, Turner, Borrowdale; Simpson (Best, 88), Doyle, S Hughes, Tabb; Adebola (Kyle, 74), Mifsud. Substitutes not used: McNamee, M Hughes, Thornton.
Referee: K Stroud (Hampshire).
Booked: Wolves Breen, Henry; Coventry Doyle, Borrowdale, Mifsud, Kyle.
Man of the match: Kightly.
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