The Blades will have been disappointed only to draw this game, having being 3-0 up just after the hour mark at Shirecliffe.
David Brooks scored, either side of Jamie Hinchliffe strike, but ultimately poor defending cost the Blades all three points the performance deserved.
Coventry started brightly and should have taken an early lead, but they were denied by an excellent save from Ramsdale, before Kelly produced a last-ditch block on the rebound.
United grew into the game and opened the scoring in the 20th minute, with BROOKS drilling home a free-kick from fully 25 yards.
Five minutes later, HINCHLIFFE doubled the lead, slotting past the advancing goalkeeper from Brooks's well weighted pass to put the Blades in complete commanding going into the break.
United were quickly out of the blocks in the second-half too and after a period of sustained pressure, BROOKS made it three in the 64th minute with Cockerline claiming the assist.
The home side switched off from the restart though and gave the Sky Blues a lifeline immediately. United had chances to regain the three-goal advantage, but both Hutchinson and Slew were wasteful in front of goal and those misses proved costly.
In the last 10 minutes the visitors put the hosts under some serious pressure and from a Ramsdale spill, Coventry made it 3-2 from close-range with the striker scoring on the rebound.
United continued to be under the cosh, but looked to have seen the job through, until the final kick of the game, when City scored the equaliser in the 94th minute, to leave Coach Travis Binnion bitterly disappointed.
He remarked: "We were worthy of our three-goal lead, but you have to be winning games from those positions.
"We missed chances to kill the game off and poor defending and individual errors cost us goals at the other end.
"You have to defend properly from the first whistle to the last, even when you are tiring, that is something we must learn quickly."
Blades: Ramsdale, Brown, Charlesworth, Ishmail, Evans, Kelly, Brooks (Semple 88), Ramsey (Hutchinson 69), Cockerline, Slew (Burton 82), Hinchliffe.