Frank Lampard's side had seen their unbeaten start to the season ended in a surprise loss at Wrexham on Friday.
The Sky Blues were in trouble again when Sam McCallum put the Blades ahead in the first half at the CBS Arena.
But Tatsuhiro Sakamoto, Bobby Thomas and Brandon Thomas-Asante scored in a second half goal spree that secured Coventry's ninth win this season and lifted them four points clear at the top.
Luke Ayling's stoppage-time header salvaged third-placed Middlesbrough's 1-1 draw at Leicester after Jordan Ayew converted a first-half penalty for the hosts.
Languishing in 13th place after last season's relegation from the Premier League, Leicester were booed off for a second successive home game following last weekend's defeat against Blackburn.
Lewis Baker scored twice as Stoke crushed Oxford 3-0 at the Kassam Stadium to move up to second place.
Sonny Carey hit Charlton's stoppage-time winner as they defeated West Bromwich Albion 1-0 at the Valley to move back into the Championship play-off places.
Charlton captain Greg Docherty's first-half penalty was saved by Joshua Griffiths.
But Carey's 30-yard drive deflected under Griffiths as Charlton extended their unbeaten run to five league matches.
Birmingham recorded a 4-0 victory for the second time in four days as they thrashed Millwall at St Andrew's.
Chris Davies' side were in clinical form as they followed up Saturday's thumping of Portsmouth with another impressive win on home turf.
Ipswich fought back to rescue a 1-1 draw against Watford at Portman Road.
Imran Louza netted for Watford after 16 minutes, but Jaden Philogene grabbed Ipswich's equaliser soon afterwards to leave both teams in mid-table.
Lars-Jorgen Salvesen's first goal for Derby sealed a 2-1 win against Hull at Pride Park, while Yuki Ohashi fired Blackburn to a 1-0 victory at Bristol City.