Rowan Vine's 11th of the season and a stunning Dean Morgan free-kick gave Town the win against the Sky Blues and spared the blushes of Ahmet Brkovic, who netted at both ends.
The Croat put the Hatters 1-0 ahead completely against the run of play with a dipping 20-yard effort on the stroke of half-time.
But he then diverted a header past Dean Kiely on the hour to put the visitors level.
Luton were thankful for a man-of-the-match performance from Kiely, who kept his side in the game with a string of superb first-half saves.
The game kicked off amid gloomy conditions and Luton were the first to sniff out an opening in the fourth minute. Mikkel Bischoff completely missed Steve Robinson's curling pass down the left channel allowing Vine to run in on goal and hit an angled 20-yard drive that Luke Steele gathered at the second attempt.
The visitors though gradually took control and, after Leon Barnett had moved quickly to stop Leon McKenzie running on to Michael Doyle's tenth-minute pass, Stern John tested Kiely with an 18-yard snap-shot seconds later.
The Sky Blues' former West Ham man Elliott Ward then went close with an eight-yard header from a Stephen Hughes corner that flashed just past the post in the 21st minute.
Kiely then had to be alert to block McKenzie's effort from point-blank range after Bischoff had headed on Richard Duffy's deep free-kick into the box.
The Hatters continued to be pressed back and Duffy was next to try his luck with a 20-yard right-foot volley that whistled a foot wide after Kevin Foley had half-headed clear from the full-back's initial chip into the penalty area.
Coventry kept coming and only a miraculous double save from Kiely kept the game goalless in the 31st minute. Foley lost the ball far too easily to McKenzie on the left, and the former Norwich man crossed for Dele Adebola to flick on for John, whose six-yard header was blocked by Kiely.
Then, as the ball fell for Colin Cameron, Luton's on-loan Portsmouth stopper somehow blocked the rebound, before Cameron then sliced over on the stretch.
Another Coventry attack saw McKenzie head straight at Kiely from ten yards in the 34th minute from Hughes' free-kick on the right.
Luton finally got their act together a minute before the break when Lewis Emanuel's driving run down the left led to Lewis Edwards hitting a 25-yard shot that deflected into the path of Vine, who slid the ball home only to be ruled offside.
In stoppage time Kiely continued his heroics with a superb fingertip save to tip Hughes' curling 30-yard free-kick over the bar.
Incredibly the Hatters went into the break a goal up when they scored in the second minute of added-on time completely against the run of play.
Brkovic, who had been largely anonymous for most of the half, dispossessed Cameron and held off Bischoff before despatching a dipping 20-yard effort that went over Steele and nestled in the far corner of the net.
The second period began quietly with a 30-yard Cameron effort and a deflected Vine shot all to show from the first ten minutes of action.
Steele was then called into action in the 57th minute as he pushed Brkovic's 18-yard strike past the post before Brkovic netted again on the hour - only at the wrong end.
The Croat was back doing his defensive duties as Luton faced up to a Hughes free-kick 40 yards out but, as the winger challenged McKenzie for the cross, the ball flicked off his head and found the back of the net off the underside of the crossbar despite Kiely almost keeping the effort out.
Town reshuffled by bringing on Chris Coyne for the ineffective Robinson, moving Barnett into midfield. And the move paid off as the Hatters scored twice in three minutes to seal the points.
Firstly Edwards, who had hardly been involved in the action, received the ball out wide in the 64th minute and crossed for the onrushing Vine to net at the second attempt.
In the 66th minute Luton were in the driving seat when Town won a free-kick for a Hughes handball and Morgan stepped up to arrow a superb drive into the far corner from 25 yards to the delight of the home faithful.
Coventry made a triple substitution as they chased the game, bringing on Adam Virgo, Darren Currie and Kevin Kyle but, apart from a 25-yard Hughes shot well fielded by Kiely late on, they never looked like fighting back.