Haji Wright scored twice to complete a second half turnaround for the Sky Blues at the Coventry Building Society Arena.
Millwall took the lead midway through the first half, when Romain Esse’s shot deflected off Luis Binks and past Brad Collins.
However, a two-minute spell in the second half saw Wright score twice, as the Sky Blues ran away with all three points.
With a minute on the clock, Brad Collins produced a fine stop at point-blank range to deny George Honeyman from inside of the six-yard box.
At the other end, City caught Millwall with a fine move, which resulted in Milan van Ewijk pulling the ball back for Tatsuhiro Sakamoto and his shot was saved by Matija Sarkic and then it fell to Haji Wright on the follow-up, but his effort hit the post and was cleared off the line by Japhet Tanganga.
The game was creating chances for both sides and this time it was Michael Obafemi who Collins kept out, with his shot from just inside of the area being palmed away by the City shot-stopper.
The visitors would break the deadlock moments later and it was Romain Esse who’s shot deflected off Luis Binks and into the back of the net.
Millwall continued to attack after taking the lead and this time he was on his toes to keep out Obafemi’s shot from inside of the area.
The Sky Blues were looking for a way back in and a chance presented itself to Victor Torp with a free-kick 25 yards out, but he was denied by the hand of Sarkic.
City continued to apply pressure to the Millwall back four and a move down the right broke with Kasey Palmer getting a shot away, but it would be headed behind by Wes Harding.
HALF-TIME: Sky Blues 0-1 Millwall
The Sky Blues came out of the traps in the second half and were almost celebrating an equaliser five minutes in, but Sakamoto’s shot was well saved down to his left by Sarkic.
A double change came before the hour mark and it was Bobby Thomas and Ellis Simms who were called upon, as Mark Robins’ men looked for a way back into the game.
The Sky Blues did get their leveller and it came from the spot after Haji Wright was brought down in the area and he stepped-up to send Sarkic the wrong way and fire the Sky Blues back on level terms.
Then, minutes later, Callum O’Hare broke through the Millwall midfield and picked out Wright and his first-time strike beat Sarkic and City were in front for the first time.
That lead could have been extended further moments later, but Victor Torp’s shot deflected behind for a corner.
FULL-TIME: Sky Blues 2-1 Millwall
Goals: Romain Esse 11’, Haji Wright 67’ 69’
Yellows: Romain Esse
Reds:
Attendance: 24,168 (817)
Sky Blues Xl: Brad Collins (GK); Milan van Ewijk, Joel Latibeaudiere, Luis Binks, Jay Dasilva, Victor Torp, Josh Eccles (Thomas 56’), Callum O’Hare; Kasey Palmer (Simms 56’), Haji Wright, Tatsuhiro Sakamoto.
Unused Subs: Ben Wilson (GK), Jake Bidwell, Liam Kelly, Bradley Stretton, Matty Godden, Fábio Tavares.
Millwall Xl: Matija Sarkic (GK), Danny McNamara, Jake Cooper (C), Wes Harding, Joe Bryan, Japhet Tanganga, Casper De Norre, Romain Esse (Watmore 62’), George Honeyman (Saville 77’), Zian Flemming (Mayor 77’), Michael Obafemi (Bradshaw 62’).
Unused Subs: Bartosz Bialkowski (GK), Murray Wallace, Billy Mitchell, Allan Campbell, Ryan Leonard.