The home side cruised to victory thanks to Diogo Jota’s 17th goal of the season in the 21st minute and an 87th-minute strike from Benik Afobe.
They played the final 38 minutes with a one-man advantage after the Blues had been reduced to 10 men when Harlee Dean was sent off for bringing down Helder Costa.
The Portuguese, who now wants to break the 100-point barrier on the way to winning the Championship title in his first season in charge, said: “I am very pleased. This is a big moment, first for the fans. It is why we work, for our fans.
“It was a special feeling always having the fans behind us.
“The players have been fantastic from day one. But we know that we still have something to go for and this season does not deserve any bad moment.
“It was a very hard season but the players deserved (to be promoted). They believed in something that was changing.
“They trust and believe and they kept doing that. It is the best reward you can have when someone believes the same as you.
“We now have 95 points, let’s get more and achieve some kind of glory.”
Nuno allowed his players to celebrate with a drink in the changing room after the game and he added: “That is something I have never allowed (before). It was the first time.”
Birmingham boss Garry Monk is facing a real fight to avoid relegation as his side are only two points above the drop zone with three games remaining.
Monk admitted the miss by Maxime Colin in the 11th minute was crucial but insisted his side will keep fighting.
He said: “We had that great opportunity with Max and then in the second half going down to 10 men made a difficult challenge much harder.
“We had a chance at the end through Lukas (Jutkiewicz) to snatch an equaliser but that is the difference. Wolves were clinical.
“But we are fighting. We are not going to take our eyes off the prize. These players are giving everything and will keep fighting.
“We knew this game would be difficult. We came to make it difficult and I thought we did that in the first half.
“With 10 men we were still in the game. It is very clear we are fighting and we have three massive games to come. It is still in our hands.
“We believe the belief will get us to where we want to be.”
Monk plans to appeal Dean’s dismissal and he added: “Harlee made an attempt for the ball. We will be looking to get that rescinded.”
Arsenal extended their poor form away from home with a 2-1 defeat to Newcastle United.
Matt Ritchie scored the winner as the Magpies went past the 40-point mark, 13 clear of the relegation zone. Ayoze Perez had earlier equalised in the first half after Alexandre Lacazette gave the visitors the lead.
The defeat leaves Arsenal in sixth place, just two points above Burnley and with plenty to ponder.
AUBA AIDS LACAZETTE
When Arsenal signed Pierre-Emerick Aubameyang in January, it didn’t seem to bode well for Lacazette whose inconsistency had already put him under pressure. With one of the most prolific strikers joining the Gunners, the Frenchman’s place during his first season at the Emirates Stadium came under serious threat, especially given Arsene Wenger’s preference to field a system with one up front.
However, against Newcastle, the two strikers showed that they can coexist. Starting together for the first time, Aubameyang was deployed on the left side but played as a narrow left winger with Lacazette through the middle. The former Borussia Dortmund hitman did well to tee up his team-mate for the opening goal.
Aubameyang’s arrival has lightened the goal-scoring burden on Lacazette, bagging six goals in seven league appearances. If Wenger can get the duo firing alongside each other on a regular basis, both halves of the £113 million partnership can thrive.
Arsenal managed to secure the win against Southampton at home last week but even then, their defending was hardly convincing as the Saints struck twice. After conceding another two against the Magpies, they have now leaked six goals in their last three games in all competitions.
Shkodran Mustafi is supposed to be an experienced head in that back-line but he has been just as guilty as anyone else of lapses in concentration. For a second time in a week he was beaten by a run at the near post with Perez this time the benefactor.
With Atletico Madrid to face in the semi-finals of the Europa League, Wenger will have to tighten things up at the back.
Arsenal are the only team in England’s top four leagues not to win an away game in 2018. Let that sink in. Their form on the road is becoming increasingly worrying as they have now lost five consecutive away games in the Premier League for the first time in their history.
It’s understandable that Wenger has chosen to put all his eggs in the Europa League basket but carrying on the way they have in the league cannot bode well for their confidence. It’s an unwanted record such as this that can have a toxic affect on the squad and seep into their campaign in Europe as well.
Jose Mourinho’s men will be looking to keep up their recent form ahead of the FA Cup semi-final with Tottenham next week while the Baggies need a miracle to avoid the drop.
Follow all the football with our live blog: