The Blades were looking for a fourth straight win against Coventry and started well.
But they suffered a telling blow when Baxter was shown a straight red card for a poor tackle.
And to make matters worse, the Blades fell behind when Dominic Samuel got the wrong side of Bob Harris, before slotting the ball under the grasp of goalkeeper Iain Turner.
Manager Nigel Clough brought on Terry Kennedy at half-time, but any changes went out of the window as Coventry quickly doubled their lead at the start of the second half.
And again it was the impressive Samuel who netted in front of the 1,000 travelling City fans.
United had numerous chances to score, before two goals in quick succession brough the scores level.
First Michael Doyle pounced after an amazing goalmouth scramble.
Then Jamie Murphy struck from long range to great celebrations from the United fans.