The 21-year-old Rogers had only been on the pitch 13 minutes when he fired home in the 89th minute to earn Michael Carrick’s team a fifth straight Championship win.
The result moves the hosts just one point behind his former team-mate Rooney’s seventh-placed City, who lost for a fourth game in a row on the road.
It looked like the ex-Manchester United and England pair would have to settle for a point on Rooney’s debut in the Birmingham hot seat, but substitute Rogers had other ideas.
Rooney was greeted with a mixed reception on his return to an English touchline, with Boro’s fans quick to direct a derogatory chant his way while the Blues’ contingent chanted his name.
“It was a big goal for all of us – a big goal to win a game,” said a delighted Carrick.
“I’m really pleased for Morgan, he came on to make an impact. Goals like that can give you a massive boost and I am sure he will have an impact for the rest of the season.
“We did enough to win the game because we had enough chances, and those chances we could have scored from, they were good ones.
“I couldn’t fault the boys. It is tough when you go into a game like this because we didn’t really know what we were going into, there wasn’t much we had to go on (after Rooney’s arrival).
“But I’m really pleased about the impact from the boys off the bench. They have all come off and made an impact in different ways.
“You never know if a goal is going to come, but you have to keep doing the right things and freshen up to try to create a spark. In the end the boys found a way to score.”
His former Old Trafford team-mate added: “I have been quite calm. You always have a feeling before the game as player or manager, which is normal, but I was quite calm. I know what I want.
“I know where we need to get to. I knew this was a possibility today, but it will take time to get where we want to go.”
Middlesbrough: Dieng, Smith (Forss 81), Fry, McNair, Engel, Barlaser (Howson 76), Hackney, I Jones, Crooks, Greenwood (Rogers 76), Coburn (Latte Lath 66). Unused substitutes: van den Berg, Dijksteel, Silvera, Glover, Ban gura.
Birmingham City: Ruddy, Drameh, Sanderson, Long, Longelo, Sunjic (James 83), Bielik, Gardner (Bacuna 61), Stansfield (Jutkiewicz 83), Hogan (Miyoshi 70), Dembele (Burke 62). Unused substitutes: Etheridge, M Roberts, Aiwu, Donovan.
Referee: Rebecca Welch (Washington).