The Blades began the night behind previous leaders Leeds only on goal difference and took another step towards an immediate return to the Premier League.
Gustavo Hamer held his hands up in apology to the travelling fans after opening the scoring against his former club with a stunning free-kick on 19 minutes.
Tyrese Campbell turned in his 10th goal of the season to double the home side's lead from Femi Seriki's cross before half-time.
Rhian Brewster then completed a comprehensive win by smashing in his first goal at Bramall Lane since 2022.
Jack Rudoni pulled a goal back in stoppage time but Coventry remained in fifth after just a second defeat in eight games.
Leeds have the chance to retake top spot when they host Swansea on Saturday.
But Chris Wilder's men have opened up a five-point lead over third-placed Burnley in the race for a top-two finish that will secure promotion to the Premier League.