The message flashed up at regular intervals on the advertising hoardings all around the ground. As part of a promotional campaign for Nike, players have been asked to come up with a pledge for the new season. Wayne Rooney’s is quite simple: score more goals.

For a player who was slow to get off the mark in the previous two seasons, there could be nothing more satisfying than a goalscoring start to the new Barclays Premier League campaign. Last season it took him until September 27 to get off the mark for Manchester United. The previous year, when he was hampered by injury, it was October 2.

This time his season was only 34 minutes old when he headed Nani’s cross against the post and, reacting quickly, swept in the rebound, ensuring that the champions followed Chelsea and Arsenal in launching their season with a win.

The first game of the season, at home to Birmingham City, is not the context in which to draw meaningful conclusions about United’s prospects in the post-Cristiano Ronaldo era, but, with Antonio Valencia making little headway and Dimitar Berbatov showing few signs that he is ready to raise his game, it was just as well for Sir Alex Ferguson that Rooney hit the ground running yesterday.

Too many of his team-mates were plodding, but, with eminently winnable games against Burnley and Wigan Athletic to follow this week, there is time for United to get into their stride — and, Ferguson hopes, to get at least one of his injured defenders fit — before the subsequent tests against Arsenal, Tottenham Hotspur and Manchester City.

There are plenty of reasons to wonder whether, after winning three successive Premier League titles, this may not be United’s year, but Rooney is adamant that it will be his.

In an interview in these pages during the summer he suggested that it is time, at the age of 23, for him to follow Ronaldo by going “from someone who could be a great player into someone who is a great player”. He also spoke of “grabbing the season with both hands” and, significantly, of his desire to be played “in my right position”.

Rooney was required to make sacrifices to accommodate Ronaldo, but this season he will be a central figure for United in more ways than one. It is a heavy burden for a young player who has not always lived up to his belief that he is a natural goalscorer, but the responsibility did not weigh on his shoulders yesterday as he scored the all-important goal, forced Joe Hart into two awkward saves and set up opportunities from which Berbatov and Michael Owen, a late substitute, should have done better.

There were three highly encouraging aspects to the goal. The first is simply that he was there, lurking in the penalty area. The second is that he leapt so well to head the ball against the post. And the third is that he reacted so quickly, ahead of Franck Queudrue, to poke the loose ball past Hart. It was, at the risk of tautology, a goalscorer’s goal.

For Birmingham, it was unfortunate. It had seemed that they had weathered the worst of the storm in the first 15 minutes, when Hart, the goalkeeper on loan from Manchester City, made excellent saves from Berbatov, Nani and Rooney. It was an impressive debut for Hart, but he was also well served for the most part by his central defenders, Queudrue and Roger Johnson. Ferguson observed that Birmingham’s resolve could be seen in the number of goalbound shots that their players blocked. It is, as he said, an encouraging sign for Alex McLeish, their manager.

Birmingham’s game plan did not extend much beyond containment, even after Rooney’s goal, but on the rare occasions they ventured forward, they threatened United’s depleted back four.

James McFadden twice stepped in from the wing to curl shots that brought McLeish to his feet. Cameron Jerome struck a shot that whistled just past the post. Queudrue had a header cleared off the line by the excellent Patrice Evra.

Christian Benítez, making his debut as a second-half substitute, sprang the offside trap in the 78th minute and cut inside Wes Brown’s challenge before seeing a shot well saved by Ben Foster, who looked far more assured in the United goal than he had in the Community Shield seven days earlier.

There were, of course, more opportunities at the other end, the best of them falling to Owen when Rooney sent him clear in stoppage time. It was the type of chance he has converted on countless occasions, but this time he fluffed his lines, seeing his shot saved by Hart. He looked skywards, aware of the difference a goal on his home debut would have made.

The former Liverpool forward had been received warmly by the Old Trafford crowd, but some coldness remains, as could be seen in the pages of the latest copy of Red Issue, the fanzine, where he was referred to as “the Welsh dwarf”.

The solution for Owen is simple: to score goals. It is the solution to everything for United this season, from Rooney’s ambitions to life after Ronaldo.

There was only a solitary offering yesterday, but, on this occasion, it was enough.

Manchester United (4-4-2): B Foster 7 — Fábio Da Silva 6 J O’Shea 7 J Evans 5 P Evra 8 — A Valencia 5 D Fletcher 7 P Scholes 6 Nani 6 — D Berbatov 6 W Rooney 8. Substitutes: R Giggs 6 (for Nani, 46min), W Brown (for Evans, 74), M Owen (for Berbatov, 74). Not used: T Kuszczak, R de Laet, D Gibson, Anderson. Next: Burnley (a).

Birmingham (4-1-4-1): J Hart 7 — S Carr 6 R Johnson 7 F Queudrue 6 G Vignal 6 — L Carsley 6 — S Larsson 5 B Ferguson 6 K Fahey 6 J McFadden 7 — C Jerome 6 . Substitutes: G O’Connor 5 (for Jerome, 65min), C Benítez (for Carsley, 74), J O’Shea (for Larsson, 82). Not used: M Taylor, S Parnaby, G McSheffrey, K Phillips. Next: Portsmouth (h).

Referee: L Mason Attendance: 75,062