The Canaries did not have things all their own way at Carrow Road, with Rotherham going in at the break one up thanks to a 10th minute goal from Richie Towell, who latched on to a loose ball after Tim Krul could only parry a Will Vaulks shot.
But the hosts took complete command in the second half and never looked back after youngster Todd Cantwell had fired home his first senior goal on 55 minutes following good work from Teemu Pukki.
The Canaries deservedly made it 2-1 in the 70th minute when Cantwell floated in a cross for an onrushing Aarons to open his league account and rounded off the win six minutes from time, with Pukki scoring his 12th of the season after defender Semi Ajayi had been caught in possession.
“In the end I thought Norwich deserved the win – they created enough chances to have won the game comfortably,” Warne 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.”
Norwich boss Daniel Farke was impressed with the way his side responded to an early setback
“It was a difficult start for us today and it was then important that we showed the right mentality, especially after the draw at Hull in midweek,” said Farke. “For the first 25 minutes it was tough but for the next 65 minutes I thought we were brilliant going forward and at the back we didn’t allow them a single chance.
“In the end I think it was a well deserved win and I think we could easily have scored five of six goals with all the chances we created.”
Norwich City: Krul, Aarons, Zimmermann, Klose, Lewis (Rhodes 87), Tettey, Vrancic (Trybull 89), Emi, Stiepermann, Cantwell, Pukki (Godfrey 90). Unused substitutes: Marshall, Passlack, Srbeny, McGovern.
Rotherham United: Rodak, Vyner, Ajayi, Robertson (Wood 46), Mattock, Vaulks, Forde (Proctor 73), Williams, Newell (Taylor 42), Towell, Smith. Unused substitutes: Price, Manning, Wiles, Jones.
Referee: S Martin (Staffordshire).