Frank Lampard's side took the lead in the 11th minute when former Millwall winger Romain Esse squeezed a shot over the line from close-range.
It was Esse's first goal for the Sky Blues since joining on loan from Crystal Palace earlier in January.
Fifth-placed Millwall equalised through Serbian striker Mihailo Ivanovic's flicked finish from Femi Azeez's cross in the 28th minute.
But Ivanovic wasted a golden opportunity to put Millwall ahead in the second half and Haji Wright poked in Coventry's 78th-minute winner after the visitors failed to clear Tatsuhiro Sakamoto's cross.
Coventry are eight points clear at the top as they chase promotion to the Premier League.
Marvin Ducksch and Kyogo Furuhashi fired Birmingham to a 2-0 victory at Sheffield Wednesday, who set an unwanted club record.
Ducksch broke the deadlock in the 83rd minute and Furuhashi sealed Birmingham's first league win on the road since October with a second goal in stoppage time.
Bottom of the table Wednesday's winless league run has reached 21 matches, the longest in the club's history and also a record in the Championship era.
Wednesday, docked 18 points in total after going into administration and further financial breaches, are still waiting for new owners to be confirmed.
A consortium led by sports analytics businessman James Bord was reportedly chosen as preferred bidder last month, while another interested party, former Newcastle owner Mike Ashley, is waiting in the wings.
Ipswich moved into second as Jack Clarke's double inspired a 2-0 win over Bristol City at Portman Road.
Kieran McKenna's team are one point above third-placed Middlesbrough, who travel to Stoke on Wednesday.
West Bromwich Albion were plunged into a relegation battle as fellow strugglers Norwich won 5-0 at the Hawthorns.
Oscar Schwartau put Philippe Clement's side ahead in the 16th minute.
Second-half goals by Ali Ahmed, Anis Ben Slimane, Ben Chrisene and Mathias Kvistgaarden condemned Albion to a fourth successive league defeat and an eighth loss in their last 10 games.
Third-bottom Norwich climbed to within one point of West Brom.
Derby boosted their play-off ambitions with a 2-1 win at lowly Charlton.