Chris Armstrong's headed goal in the 61st minute gave United their second win this week and put them above Coventry in the Championship table.
Coventry manager Iain Dowie made three changes to the team who drew with nine-man Scunthorpe at home on Tuesday night, while Bryan Robson stuck with the same side who thumped Charlton 3-0 at The Valley.
The game had a slow start, with neither team testing the goalkeeper until the 23rd minute.
David Carney played a tidy ball to Armstrong on the left-hand side of the area. Armstrong hit a bouncing shot towards Dimi Konstantopoulos' goal, which the Greek palmed away for a corner.
City's first attempt came in the 33rd minute when a moment of class from Dutch midfielder Ellery Cairo nearly gave his side the lead. Cairo turned on the edge of the box, and hit a half-volley towards to top of the net - only for Paddy Kenny to turn over for a corner.
And City could have taken the lead before half-time when a through ball saw forward United's Gary Cahill slip, leaving Dele Adebola one-on-one with Kenny, only for the veteran to put his effort wide.
United looked brighter in the second half and the dangerous combination of James Beattie and Keith Gillespie threatened.
Gillespie's free-kicks in the 57th and 60th minutes had given Beattie two opportunities to grab his 13th goal of the season, with the striker's headers coming close.
And Beattie turned provider a minute later after finding space on the right. His cross to Chris Armstrong was measured, and the defender's powerful header found its way past the keeper after a deflection.
United continued to press for a second, with Gillespie hitting the sidenetting on 74 minutes.
Coventry had brought on Leon McKenzie in the 64th and Wayne Andrews in the 80th to try and change the game.
But despite some promising build-up, City failed to test the keeper and United held on for the win.