Manchester United put their foot down to accelerate away from Manchester City and stretch their lead again at the top of the Premier League table to seven points with this victory.

It was close, though. The second half was dominated by Southampton who bombarded United's penalty area throughout and David De Gea, who was again inconsistent, had to produce an impressive save from a late Rickie Lambert free-kick to protect their lead.

The goalkeeper's nervousness had been evident when he spilled an earlier 25-yard free-kick from Southampton's captain, a shot that barely moved in the air, and United were fortunate not to concede the equaliser.

"We tried to play the way we normally play but found it difficult because the pitch had dried out a lot," said Sir Alex Ferguson. "But in the second half Southampton put in the best performance anyone has here this season."

On 75 minutes Robin van Persie thought he had made it 3-1 with a shot from a Wayne Rooney pass that was hit with the outside of the England forward's boot but it was ruled offside.

Had the "goal" stood United might have enjoyed a less frantic finale and Ferguson's side can be thankful they emerged with all three points. The manager conceded the point, adding: "If you look at it, in my experience when you are going for championships there's always a game when you say we were a bit lucky – and I think this was one of those nights."

United were rocked almost instantly by the kind of howler all managers detest. Addressing a run of league fixtures that started with this one and, Everton apart, included the lesser lights of Fulham, Queens Park Rangers, Norwich City, West Ham United, Reading and Sunderland, Ferguson had written: "Let's not fool ourselves into believing that we are now entering a phase against the lower teams that will present us with easy pickings. That would be a rubbish attitude."

That may have been the adjective used to describe his side's start. The Scot had hardly been sitting for two minutes when Michael Carrick's poor back-pass was compounded by De Gea whose indecision meant he stuck out a tentative leg rather than emphatically clear the danger. From a close angle Jay Rodriguez made it 1-0.

"Michael's pass-back was a bit soft and Michael held his hand up," said Ferguson. "It's great to see that, honest players like Michael saying: 'Sorry boss, sorry lads.' It's great."

Within five minutes United were level. Carrick, who recovered from his helping hand in Southampton's goal to snap into the tackle and zip around midfield, played a pass that was deflected into the path of Shinji Kagawa. The Japan forward slid a ball behind the defence and Rooney slotted it confidently past Artur Boruc.

Now United swarmed all over Southampton and by 26 minutes were ahead, Rooney again the scorer. When Van Persie swung a free-kick in from the right that was precisely placed on Patrice Evra's head, the left-back glanced the ball back across goal and Rooney tucked it into the net.

It had been coming. Before and after the forward's 10th United goal of the season, the home side piled up the missed chances. Kagawa hit Boruc's right post from near in after Rooney dinked the ball through to him and a Van Persie cross-shot might have gone anywhere but went for a goal-kick. The centre-forward's run down the left ended with him turning the ball inside to an onrushing Evra but Southampton managed to halt the full-back's progress. Finally in the first-half assault on Boruc's goal Kagawa's smooth swivel and lay-off to Van Persie found the striker in space but he smashed his shot over the bar.

Ferguson made four changes from the team that had trounced Fulham 4-1 here on Saturday. In came Nemanja Vidic, Danny Welbeck, Kagawa and Van Persie, for Rafael da Silva, Nani, Ryan Giggs and Javier Hernández, the latter suffering from a hip injury which should clear in time for Saturday's trip to Fulham according to his manager.

Mauricio Pochettino, whose second game in charge of Saints this was following the ruthless sacking of his predecessor, Nigel Adkins, spent the half standing up in the technical area, and could be pleased with his side's start the start to the match and how, after soaking up pressure, they threatened to head home with at least a point.

"I'm very proud [of Ferguson's praise]," Pochettino said. "It's very important for my players to hear. But we leave with no points. We did play well but I'm upset at not getting a draw at least. It doesn't console me. I think in the second half we played as we should have done for the whole game."