The Hatters held a 2-0 lead at halftime thanks to a penalty from Carlton Morris and a goal from Elijah Adebayo, his second in as many games.
Ellis Simms powered home a header and Victor Torp's spectacular effort got City back on level terms before Haji Wright bundled home a winner after Tom Holmes had been sent off.
It proved to be just a second win in 10 league outings for Mark Robins' side, who lifted themselves out of the bottom three in the process.
Morris' penalty came against the run of play after a strong start from Coventry.
TrendingA clever corner routine from the hosts led to Ben Sheaf's flick giving Tatsuhiro Sakamoto a sight at goal which was blocked by the onrushing Adebayo, before Josh Eccles' follow-up was pushed away by Thomas Kaminski.
Kaminsi was also called upon to save Milan van Ewijk's strike from distance before Simms diverted Eccles' free kick wide.
Sheaf then fired into the side netting after van Ewijk's cut-back, but at the other end Sakamoto got himself in a tangle and brought down Tahith Chong in the box.
Morris stepped up to net his fourth of the season from the spot.
Luton almost doubled their lead through Chong, who took advantage of the space vacated by the stricken Bobby Thomas before turning and shooting, but his effort was brilliantly tipped round the post by Oliver Dovin.
Simms, who had only scored once in the league this season, glanced van Ewijk's corner wide as Coventry looked for an immediate reply.
Luton extended their lead before half time when Tom Krauss played in Adebayo and the forward netted his second of the season by smartly lifting his effort over Dovin.
Robins' side came out all guns blazing after the interval as they looked to reduce the arrears, firstly through Wright, who headed a dangerous cross from the right wide before seeing an effort deflected over the crossbar.
Kaminski was in the action once again as he saved Sheaf's long-range effort, but he could do nothing to stop Simms powering home Jack Rudoni's in-swinging corner.
Eccles whistled a shot wide for the hosts whilst Wright chopped inside and forced Kaminski into another save for the visitors.
Coventry had their equaliser through Torp, who curled in a spectacular effort from outside the box which crashed in off the inside of the post.
Holmes' red card as the clock hit 90 minutes spurred the Sky Blues on to grab their winner as Wright bundled in on the line despite the best efforts of Kaminski, giving Coventry a well-deserved win.
Coventry's Mark Robins:
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Luton's Rob Edwards:
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