A last-ditch Jay Bothroyd goal stunned Grimsby after an explosive second half at Highfield Road.
The visitors offered little in the first half but their two goals after the break almost ensured the honours were shared.
Bothroyd had the ball in the back of the net after seven minutes when he latched on to Dean Gordon's throughball but his cool finish was ruled out for offside.
Moments later Stacy Coldicott had a good effort from 25 yards saved as Grimsby looked to ease the pressure.
But the Sky Blues kept pouring forward; first John Eustace failed to get enough purchase on a Gary McAllister cross, then Bothroyd came up with the best effort so far.
The young striker controlled a long Morten Hyldgaard clearance and turned Steve Chettle neatly on the edge of the box, unleashing a powerful shot that just rose over the crossbar.
McAllister's men then spurned plenty of chances to take the lead as Grimsby held on until half time.
The second half was an infinitely better spectacle as Grimsby instantly took advantage of some lax defending.
After 47 minutes Steven Kabba raced through as the defence was caught flat-footed and his tidy finish went through Hyldgaard's legs.
But Coventry kept their heads up and just 20 seconds later they equalised. Bothroyd's cross found the dangerous Lee Mills who climbed well to level the scores.
Coventry were well on top when they were awarded a soft penalty after 69 minutes; Mills tumbled under a Coldicott challenge and McAllister easily converted the spot-kick.
But it was Grimsby's turn for a quick response when, seconds later, Stuart Campbell's cross was met by Alan Pouton whose downward header bounced high and deceived Hyldgaard.
But man-of-the-match Bothroyd had the final say with a superb header on 87 minutes to break the visitors' hearts