Nemanja Vidic's late header gave Manchester United victory in a tight encounter with Everton.
Nemanja Vidic celebrates his winner for Man Utd with Rio Ferdinand
The home side and United were closely matched until Vidic arrived at the near post to power home Nani's corner after 83 minutes to seal a crucial win.
Paul Scholes had earlier wasted United's best opportunity, volleying over from 10 yards.
But he rescued United just after half-time when he scrambled Andrew Johnson's header off the line.
United again struggled to mount any serious attacking threat but Vidic's goal gave them their third successive 1-0 win.
Manchester United kept Wayne Rooney, fit after a broken foot, on the bench but Cristiano Ronaldo was able to return after suspension.
Everton were without former Old Trafford keeper Tim Howard, who dislocated a finger playing for the United States against Brazil, so summer signing from FC Cologne, Stefan Wessels, was handed his debut.
But the German and opposite number Edwin van der Sar were barely troubled in a first 45 minutes in which chances were at a premium.
Carlos Tevez played three clever passes in the opening stages but Everton held firm, with Joleon Lescott an imposing figure.
Everton left-back Leighton Baines was crudely hauled down by Michael Carrick after racing into the area but even though the home fans screamed for a penalty, the offence was clearly outside the box.
Vidic wasted United's best chance on the half-hour when he turned wide at the near post after Everton's defence failed to deal with Ryan Giggs' corner.
United suffered a blow five minutes before half-time when Mikel Silvestre collapsed with no-one near him and he was carried off with what appeared to be a bad knee injury, to be replaced by Nani.
Scholes was walking a tight line after being booked by referee Alan Wiley for throwing the ball away and he was fortunate not to be sent off for a late challenge on Mikel Arteta just before the interval.
Everton started the second period well and Scholes was forced to hack Johnson's header off the line when he flicked on Arteta's corner.
Scholes wasted the best opportunity of the match after 53 minutes when he volleyed over from only 10 yards from Tevez's flick, with Everton's defence nowhere.
Ronaldo was booked for diving as the atmosphere hotted up, tumbling under a challenge from Leon Osman on the edge of the area.
Everton made a double change, sending on Victor Anichebe and Steven Pienaar for Osman and the tiring Yakubu.
But it was United who made the breakthrough with seven minutes left, Vidic powering home Nani's corner at the near post.
Everton sent on Scotland's midweek hero James McFadden in the closing minutes and he instantly brought a fine save from Van der Sar, with Joseph Yobo unable to turn in the rebound.
Everton manager David Moyes:
"I thought our boys did very well. It's disappointing to lose a goal from a corner at any stage, but especially in the last few minutes.
"We've got a big week coming up with a Uefa Cup tie, so I don't want us to feel too down after this.
"Our forwards caused them problems but their defenders played very well."
Manchester United manager Sir Alex Ferguson:
"We are delighted with the win because people will see a very improved Everton this season. Teams will find it very hard coming here.
"But we stood up to Yakubu and Andrew Johnson, who will be handful for anyone, and our defenders showed great determination.
"Nemanja Vidic is a marvellous defender but he can get a goal as well. It's a bit of a concern that we are not scoring as many goals as we want, but until we get everyone back we will play like this.
"We are determined, we have a good team ethic, we have got a good shape and we had good passing. We will work away and this is a very good result."
Everton: Wessels, Hibbert, Yobo, Lescott, Baines, Arteta, Jagielka, Neville (McFadden 85), Osman (Pienaar 73), Johnson, Yakubu (Anichebe 74).
Subs Not Used: Turner, Carsley.
Booked: Neville, Pienaar.
Man Utd: Van der Sar, Brown, Ferdinand, Vidic, Silvestre (Nani 41), Ronaldo, Carrick, Scholes, Evra, Giggs (Saha 63), Tevez, Nani (Pique 85).
Subs Not Used: Kuszczak, Gibson.
Booked: Scholes, Ronaldo.
Goals: Vidic 83.
Ref: Alan Wiley (Staffordshire).