The England striker headed a cross from Nani against the post and the ball came back for him to tap into an empty net in the 34th minute at Old Trafford. United is trying to become the first topflight English team to win the league title four seasons in a row.
"We created plenty of chances to win the game and thankfully we came out with the three points," Rooney said. "While it was 1-0 there was still a chance (Birmingham) could get a result. The first games of the season are always difficult."
Michael Owen came on as a substitute for the last 16 minutes and should have marked his first Premier League appearance for United with a goal in injury time when he broke clear of the Birmingham defence from Rooney's flick-on, but his shot was deflected wide by Birmingham goalkeeper Joe Hart.
"Owen made a great run and the keeper made a great save," said United manager Alex Ferguson. "But he will get his goals, no question about that.
"I know some of our supporters are still worried that I have not bought a megastar to replace Cristiano (Ronaldo)," Ferguson said. "They are concerned because they can't quite work out how we are going to compensate for all the goals Cristiano used to get for us. But I am more than happy with our squad and although we have lost a major player, I believe we are on the threshold of a very exciting era for Manchester United."
United opened the campaign without regular center backs Rio Ferdinand and Nemanja Vidic. Vidic was already ruled out with a calf muscle injury but Ferdinand pulled out with a thigh injury which Ferguson said could sideline him for two weeks.
Although Birmingham went close to scoring three times and United goalkeeper Ben Foster made a top quality one-handed save to keep out Christian Benitez's shot in the 78th minute, Alex Ferguson's team should have won by a wider margin.
Darren Fletcher missed the target from close range just before halftime, Hart saved a 30-meter shot from Rooney and Lee Carsley cleared off the line from Dimitar Berbatov in the second half before the Bulgarian was replaced by Owen with 16 minutes to go. Minutes earlier Berbatov, appeared to be tripped inside the area by Stephen Carr.
Berbatov's former club Tottenham needed goals by two defenders to subdue Liverpool, last season's runner-up, at White Hart Lane. Having taken only two points from their first eight games last season, Spurs improved on that in their first match.
After Tottenham striker Robbie Keane had missed three simple chances against his former club, Benoit Assou-Ekotto scored his first goal for Spurs in the 44th minute with a powerful left foot shot after Tom Huddlestone's free kick had been blocked.
Liverpool captain Steven Gerrard equalized with a 56th minute penalty after Heurelho Gomes had rushed off his line and brought down Glen Johnson. But Sebastien Bassong restored Tottenham's lead with a powerful 59th header from a freekick.
Arsenal's 6-1 victory at Everton was the highlight performance of Saturday's opening day, captain Cesc Fabregas netting twice and defender Thomas Vermaelen scoring on his debut.
Manchester City justified its big preseason spending with a 2-0 victory at Blackburn thanks to a third minute strike by one of the new signings, Emmanuel Adebayor, while Didier Drogba scored twice for Chelsea, including an injury time winner, in a 2-1 victory over Hull.
In Saturday's other games, Wigan won 2-0 at Aston Villa, West Ham triumphed 2-0 at promoted Wolves, Fulham beat Portsmouth 1-0, Sunderland won 1-0 at Bolton and Stoke beat promoted Burnley 2-0.
