Wolves took the lead in the 8th minute as Leo Bonatini scored his 12th goal of the season, meeting a loose ball following a strong David Stockdale save.
Despite Wolves' first half dominance, the visitors were unable to extend their lead as Ivan Cavaleiro and Diogo Jota both went close.
Birmingham fought back in the second period but Wolves held on to win their sixth consecutive game.
Speaking after the game, Nuno revealed how he was pleased for the travelling fans.
He said: “It was a good win. This game was very important to us because of the fans. It meant a lot to them and I’m really happy for them.
“They are always, always with us and today was very important for them.
“It was a tough three points. Everybody felt that we should have done better at the end of the game.
“This is good. It shows that the boys want to improve and keep going, keep growing.
“I’m very happy because we knew tonight was going to be tough. It was a tough game but I felt that we deserved the win.
“We played last Saturday and have stayed all week without competition, we knew the results from behind, we knew that we had to come here and show that we wanted to win the game and we did it.
“We showed from minute one that we were the better team. Today we were the better team."
When asked if he felt disappointed that his side were unable to score a second goal, the Head Coach responded: “A second goal would have changed everything. It would have made us more comfortable and given us the opportunity to play better.
“We had chances so we must take credit for creating chances against a tough opponent.
“I was really happy with the first half. The way we managed and took control of the game from the first minute.
“We had good possession, we were threatening going forward and we defended very well.
“I think a clean sheet is a well deserved prize for the way we defended as a team. We didn’t concede many chances."
It was a typical derby encounter at St Andrew's, with a number of strong challenges from both sides. And Nuno felt that the referee managed the game and the occasion well.
“We analysed Birmingham before the game and saw that they were a tough team," he said.
“I thought the referee did well today. He managed the game with bookings and explained to the players why they got them.
“Tackles through the back of players can really injure them so I thought the referee did well.
“This is the circumstance of a derby."