Wayne Rooney brought a couple of smart saves from Tottenham goalkeeper Heurelho Gomes and Rafael van der Vaart also went close on two occasions for Tottenham.
But in the end the two sides cancelled each other out in a game which underlines the title race is likely to be tight right until the end.
The draw sees Tottenham, who have not beaten United since May 2001 in a run which now stretches to 24 matches, stay fifth, a point behind Chelsea and outside the Champions League places after a game which was long on effort and passion but short on quality.
The most noteworthy incident was the once concerning Rafael who was shown a yellow card for a foul on full-back Benoit Assou-Ekotto after having earlier been booked for a challenge on Wilson Palacios.
The young Brazilian raged at referee Mike Dean and kicked over a television sound boom as he left the pitch and the Football Association are likely to want to review the video. Rooney was also booked for his protests as it appeared the defender had made accidental contact with Assou-Ekotto.
Yet while Tottenham showed how far they have come under manager Harry Redknapp it was United who proved their resilience.
Ryan Giggs was named in the starting line-up for his 600th league appearance for United, just six behind the record of Sir Bobby Charlton.
Sir Alex Ferguson was also boosted by the fact that Rooney returned from an ankle injury after missing two games while Nemanja Vidic and goalkeeper Edwin van der Sar were also fit after recent absences.
Vidic's presence was crucial and he was instrumental in halting the forays of the pacy Aaron Lennon down Tottenham's right.
Due to injuries, Vidic and Rio Ferdinand have been in harness infrequently in recent seasons. There is no doubt United look more solid when they are together.
It meant Peter Crouch, who had been preferred to Jermain Defoe, for the most part was contained and that had a knock-on consequence for Tottenham in that van der Vaart was starved of the knockdowns which he has been previously so quick to exploit this season.
United might have taken the lead in the first two minutes, Rooney being neatly played in by Dimitar Berbatov but he skewed his right-foot shot across the face of the goal.
A flake of rust was suggested by that effort, although there was no sign of it after 22 minutes when Rooney, once again smartly served by Berbatov, brought a stumbling save from Tottenham goalkeeper Gomes.
United had their moments but in that first half the attacking impetus came from Tottenham and especially Gareth Bale who was beginning to give Rafael a torrid time down the left.
One of his trademark whipped-in crosses was inches away from being dispatched into the net by Crouch.
Van der Vaart looked to have cashed in on another raking cross from Bale but could only manage to send his downward header into the side-netting.
It was all fast and frantic, strewn with errors and with no time for midfield players to settle on the ball.
Not surprisingly, it was a period in which referee Dean was busy, booking Rafael, Wilson Palacios, Darren Fletcher and van der Vaart, the latter for kicking the ball away.
It needed someone like David Beckham, up in the stands and who has been training with Tottenham this past week, to put his foot on the ball and bring a measure of control.
United began the second half with more composure. They might have taken the lead after 50 minutes when Giggs's corner was flicked goalwards by Michael Carrick but sailed just wide of the post.
A minute later Rooney burst through the middle to unleash a right-foot shot from the edge of the penalty area, only to be denied by a full-length diving save from Gomes.
The Tottenham goalkeeper was certainly the busier.
It was a match with lots of attacking endeavour from both sides but no one seemed capable of creating the breakthrough.
There were claims for a penalty when Vidic blocked van der Vaart's effort after clearly holding his shirt in the penalty area but the referee waved them away.
Then came Rafael's moment of misery, at which point United were happy with their point.
Ferguson refused to comment on Rafael's red card.
"I don't need to discuss that, you can see for yourself," he said. "I don't need to discuss the referee."
Ferguson went on to praise his defenders, adding: "I think they were particularly good.
"It could be a really thrilling end to the season. Tottenham are not out of it.
"It's about winning games and keeping your nerve and (at Spurs), defensively, we kept our nerve."
Redknapp agreed with Ferguson`s assessment that the two defences had prevailed.
He said: "Both teams defended well, especially the two central defenders on their side and Dawson and (William) Gallas on ours. They were fantastic, did their jobs and made it difficult.
"Chances were few and far between. I thought we edged the game without creating too many clearcut chances. When they went to 10 men we couldn't have been more open. We were as open as a barn door going for it."
Redknapp admitted that time was running out in his bid to sign Beckham on loan. He added: "David has to be back there (America) in February and there's not a lot of time, which is a shame."