MICHAEL Smith was the last-gasp hero as Town deservedly took maximum points to keep their slim play-off hopes flickering.
Mark Cooper's men set the tone for the first half in the opening minute as a corner on the right was initially cleared but as a second-phase cross was flung in Michael Smith's close-range header was tipped over by Coventry keeper Joe Murphy.
Murphy was powerless to prevent the visitors from breaking the deadlock on eight minutes though. Nathan Byrne lifted a beautiful pass into Nathan Thompson 10 yards out. The defender struggled to get it under control but Alex Pritchard fired the loose ball home.
Callum Wilson had the hosts' first sight of goal on 18 minutes but side-footed a near-post corner wide when really he should have done better.
Pritchard nearly added his second on the half-hour mark but was inches away from getting his studs onto Jay McEveley's inswinger with Murphy flapping at air.
The keeper did better on 38 minutes to tip over Massimo Luongo's dipping effort from 25 yards.
Two minutes before the break, and entirely against the run of play, Coventry levelled as John Fleck crashed home an effort from the edge of the box - City's first shot on target.
Nathan Delfouneso then headed a foot wide as Coventry threatened to turn the game on its head before the interval.
Ben Gladwin had the first effort of note in the second period as his long-range effort had Murphy worried but bobbled wide.
Smith then had an effort charged down after Murphy committed himself at the feet of Thompson.
Coventry sub Nathan Eccleston thought he'd pinched the points with two minutes to play but his goal-bound effort was blocked by Jack Stephens. But Smith took the honours at the death, flicking a header inside the far post after a superb delivery from Thompson.