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.
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 defense from Rooney's flick-on, but his shot was deflected wide by Birmingham goalkeeper Joe Hart.
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.
Marseille is the only team not to concede a goal after the opening two rounds of the season, a sign that Deschamps is succeeding in his bid to make Marseille more competitive and tougher to score against than last season.
Marseille finished last season in second place, three points behind Bordeaux, but it dropped vital points at home.
Lille defender Mathieu Debuchy was sent off in the 64th for a second yellow card after holding back striker Mamadou Niang when he ran through on goal, but Marseille failed to take advantage and score a second goal.
Magath coached Wolfsburg to its first Bundesliga title last season, then jumped ship to sign for Schalke, which has not won the championship in 51 years.
Wolfsburg and Schalke are the only two teams to have won both of their games in the new season and have six points and identical goal difference.
Schalke dominated Sunday's match and 19-year-old Christoph Moritz, a new signing from second-division Alemannia Aachen who has been promoted to the starting lineup by Magath, opened the scoring after 38 minutes.
After Oscar de Marcos opened for the hosts in the 45th minute at the San Mames stadium, Pedro fed Xavi in the 59th for the equalizer. Pedro then sliced a long shot beyond goalkeeper Gorka Iraizoz for the winner in the 68th.
Barcelona was without Lionel Messi, Andres Iniesta and new signing Zlatan Ibrahimovic as it bids for the first of a possible six trophies this season. Barcelona beat Athletic in the Copa del Rey final last season as part of its treble together with league and Champions League triumphs.
The second leg will be played Aug. 23.
Source: AP News