Draws all round on derby day
Sunderland drew 1-1 with neighbours Newcastle United and Birmingham City and local rivals Aston Villa also shared two goals all four Premier League matches ended in stalemate.
United's eighth draw in 10 away games took them top on 45 points from 21 matches, ahead on goal difference of Manchester City, who beat Wolverhampton Wanderers 4-3 on Saturday and have played two games more.
Arsenal are third on 43, Chelsea fourth on 38 and Spurs fifth on 37. Liverpool stay 13th on 26 points, behind Everton on goal difference.
Tottenham went into Sunday's game with high hopes of securing their first win over United in 20 attempts spanning 10 years but they never did enough to unsettle the impressive visiting defence.
Peter Crouch shot just wide in the breathless early exchanges and Rafael van der Vaart sent an exquisite curler just over the bar once the game had settled.
Brazilian full-back Rafael collected his second yellow in the 73rd minute for a hotly-disputed trip of Benoit Assou-Ekotto but though Spurs threw men forward they never looked like ending United's unbeaten record this season.
"It was tight. I felt we just about edged it without being able to get the goal but I never felt we were going to get beat. It was never a game I could really see them scoring in today," Spurs manager Harry Redknapp he told reporters.
"United are very strong and disciplined at the back and hard to break down but I couldn't say at the moment they are on another level and are going to walk away with the championship.
"You can't be as good a team as you were a year ago when you haven't got (Cristiano) Ronaldo and (Carlos) Tevez. Other teams have improved and got closer to them but they've lost players like that and are still up there."
Sir Alex Ferguson thought it was a decent point for his team.
"It was a tough game, they didn't make many chances against us, we were a bit careless with our use of the ball," he said.
"Our defenders were particularly good but when we were in the final third maybe we needed a better pass."
It was a very different type of draw at Anfield, where Kenny Dalglish went through the full gamut of emotions on his emotional first home game in charge.
Liverpool, without suspended captain Steven Gerrard, produced a committed performance and deservedly led their Merseyside neighbours through a crisp strike by Raul Meireles.
Everton, though, turned the game upside down with two goals in the first seven minutes of the second half from Sylvain Distin and Jermaine Beckford.
Liverpool came back strongly and levelled through Dirk Kuyt's 68th-minute penalty after Tim Howard fouled Maxi Rodriguez.
"The players' attitude and desire to get back in the game was really something," said Dalglish, whose first two games ended in defeats by Manchester United and Blackpool.
"We could have been more than one up but we were really pleased with the way we played and that's great credit to the players who have had to adjust to the new ways of playing and training.
"There is a lot of belief coming back into the players and that is great for us"
Everton boss David Moyes admitted Liverpool were the better team in the early stages.
"I was delighted to come in only 1-0 down after the first half because Liverpool were the better team but I'm disappointed we didn't take all three points after the second half," he said.