With Leeds beating Sheffield United in the early kick-off and the Millers opening the scoring through Richie Towell in the 11th minute, the Canaries appeared to be relinquishing their position at the summit.
But Todd Cantwell's effort just after half-time triggered a turnaround as Maximillian Aarons and Teemu Pukki also found the net, the latter for the 11th time this term.
Rotherham’s Norfolk-born boss Paul Warne was disappointed his side were unable to build on their promising start to the game.
“In the end I thought Norwich deserved the win - they created enough chances to have won the game comfortably,” he said. “But we got a good set-piece goal to go ahead early on and it could have been easily have been 2-0 (when Will Vaulks hit the post).
“We gave a good, well coached side a few problems but we lost a couple of players to injury and in the second half they dominated the game, although I thought we should have done a lot better with their second and third goals. At 2-1 down with 15 minutes to go I still fancied getting something from the game, but the third goal killed us.”
Warne said he enjoyed his first experience of managing at Carrow Road, having been brought up a Norwich fan.
“I didn’t come here to lose, that’s for sure, but it meant a lot to me to manage here, “ he said.
“It was a surreal moment when I walked out through the tunnel at Carrow Road.
“My mum and dad were following the match at home because dad hasn’t been too well but a lot of my family were here to see the game and I am going off to spend the evening with them now.”