The two games started and finished a superb day of action with Liverpool ending their worst start to a season for over a century with Luis Suarez scoring a hat-trick as they won 5-2 at Norwich City for their first league win at the sixth attempt.
Elsewhere Everton continued their best start for seven seasons, Nikica Jelavic scoring twice as they came from a goal behind to beat Southampton 3-1 at Goodison Park to climb to second in the table.
Champions Manchester City also trailed but hit back to win 2-1 at Fulham with a late winner from substitute Edin Dzeko pushing them up to fourth.
Unbeaten Chelsea, who won at Arsenal with goals from Spaniards Fernando Torres and Juan Mata, have won five and drawn one and top the table with 16 points, followed by Everton on 13, United on 12, City on 12 and Spurs on 11.
At the other end, Queens Park Rangers slipped to bottom place before they meet West Ham United on Monday.
Reading came close to their first win but ended up drawing 2-2 at home to Newcastle United for whom Demba Ba scored twice.
HOODOO OVER
The most dramatic game was at Old Trafford where Spurs had not beaten United since a Gary Lineker winner 23 years ago - and not beaten them in any of their last 22 Premier League clashes home or away.
In that time they have led United on a number of occasions and 11 years ago to the day were 3-0 up against them at half-time at White Hart Lane before losing 5-3.
So despite Jan Vertonghen putting Spurs ahead after two minutes and Gareth Bale making it 2-0 after 32 minutes after a charging run and shot through the heart of the United defence, there was no taking victory for granted.
United, outplayed in the first half, controlled the game in the second after Wayne Rooney replaced Ryan Giggs and they pulled one back when Nani touched in Rooney's cross six minutes after the break, the first of three goals in less than three minutes.
Spurs replied almost immediately in the 52nd minute when Clint Dempsey fired into an empty net when United keeper Anders Lindegaard saved from Bale - but Spurs' lead lasted only one minute before Shinji Kagawa wriggled through a static Spurs defence to make it 3-2.
TREMENDOUS HOTSPUR
United then bombarded Spurs goal for half-an-hour, hit the woodwork twice and had penalty appeals turned down, but could not force the equaliser as they slipped to their second league defeat of the season.
Manager Sir Alex Ferguson told ESPN afterwards: "We made a poor start to the game and defended poorly. In the second half we were fantastic and should have got something out of the game but were very unlucky."
Spurs manager Andre Villas-Boas, whose team have not lost in seven matches in any competition since the opening day, said: "I thought we were tremendous today.
