would be his side's toughest test of the season so far, but his charges responded admirably in an entertaining encounter full of chances.
Leon Best blasted home his third goal of the season after 12 minutes before Jamie Ward levelled for the visitors in even more stunning fashion to ensure the opening 45 minutes ended level.
But the hosts were 3-1 to the good with an hour gone as Clinton Morrison capitalised on an unfortunate mistake from Nick Montgomery before Martin Cranie headed his first goal for the club.
James Harper's finish ensured a nervy final 15 minutes for the Sky Blues but United's attention will now be firmly on Friday's steel city derby against Sheffield Wednesday.
The hosts started the brighter of the two sides with the terrier-like Sammy Clingan pulling the strings in the middle of the park.
And it was he who set up the opener, floating a weighted ball over the top to find Best.
The Coventry striker brought down the ball perfectly 12 yards out before lashing an unstoppable shot past Mark Bunn from the right side of the penalty area.
Keiren Westwood did well to block Stephen Quinn's stabbed effort from point-blank range just minutes later.
Chances were coming at either end and it was up to Westwood to prove why he is regarded as one of the best goalkeepers outside the top flight with an even better save to deny Quinn for a second time when he found himself clean through.
But if Coventry's opener was impressive then United's equaliser was even better.
Ward coolly brought the ball down 30 yards from goal on the right and charged towards the area before letting fly with an unstoppable effort into the top corner that, for once, left Westwood with no chance.
On-loan midfielder Jack Cork blasted over from 18 yards for the hosts before Blades full-back Andy Taylor fluffed his lines from four yards out a minute before the interval when it looked easier to score.
There were just six second-half minutes on the clock when Coventry regained the lead.
United midfielder Montgomery failed to really do anything as the ball came towards him on the halfway line and he could only watch as it ricocheted off his body and into the path of the onrushing Michael McIndoe.
The winger burst down the left and despite his cross going behind Best and Morrison in the area, the latter readjusted his body to put a low effort past the despairing Bunn.
United immediately went in search of an equaliser and Westwood did well to tip Keith Treacy's strike around a post before Ward missed from close range.
But Coventry were almost out of sight on the hour mark as McIndoe again turned provider, floating over a corner for Cranie to head home.
Harper pounced from close range in the 75th minute to set up an edgy finale for the home faithful.
And substitute Ched Evans almost rescued a point for the visitors only to see his strike clip the top of the crossbar as the game entered the closing stages.