Spurs' 3-2 win in a thrilling match at Old Trafford saw United drop to third place and level on points with defending champion Manchester City, which needed a late goal by Edin Dzeko to grab a 2-1 victory at Fulham.
Everton is the nearest challenger to Chelsea following its 3-1 come-from-behind win over Southampton and Liverpool completed a good day for Merseyside by earning its first league triumph of the season, Luis Suarez scoring a hat trick in a 5-2 thrashing of Norwich.
Unbeaten Chelsea's fifth win in six games was secured by goals from Fernando Torres and Juan Mata and a strong rearguard display from a defence featuring John Terry, two days after he received a four-match ban for on-pitch racial abuse.
"It was a big challenge to play against a quality side like Arsenal," Chelsea manager Roberto di Matteo said of opponents who were unbeaten heading into the match at Emirates Stadium. "We were excellent. We didn't just come and sit back, we took the initiative."
On a day of 29 goals — the most in a single day in the English top flight since February — five came in the United-Spurs match, with United States forward Clint Dempsey scoring what proved to be the winner in the 52nd to pounce on a sloppy performance from United.
"It was a roller-coaster, up and down," said Dempsey, whose first goal for Spurs earned the team a third straight win and left it in fifth place — a point behind the Manchester clubs. "We found ourselves 2-0 up and then in the second half, it seemed we were chasing shadows ... But we ground out a result and showed a lot of character."
Jan Vertonghen and Gareth Bale made the most of United's sluggish start with goals in the opening 32 minutes, before Nani and Shinji Kagawa sandwiched Dempsey's strike in a crazy spell of three goals in less than three minutes.
Tottenham survived a number of good penalty shouts and late chances by United for a first win over Sir Alex Ferguson's side in 11 years.
"It was quite a game," Ferguson said. "The first half we never started, didn't get into the game. From there we were just playing against the wind."
After two straight draws and having seen Chelsea win at Emirates Stadium in the early kickoff, the pressure was on City to get back to winning ways and revive its title charge.
However, Mladen Petric put Fulham ahead in the 10th minute from the penalty spot and it needed a first goal of the season from Sergio Aguero — playing up front with Argentina teammate Carlos Tevez — to haul City back level in the 43rd.
Dzeko was thrown on in the 85th as City poured forward in search of a winner and he grabbed it within 70 seconds, slamming home after a cross from Gael Clichy was poorly cleared.
"I was worried because we continued to play well and continued to create chances, but didn't score (the winner) for 87 minutes," City manager Roberto Mancini said.
Suarez's second hat trick at Carrow Road in successive seasons helped Liverpool end a five-match winless run in the club's worst start to a season in more than a century.
"I'm not surprised because in a lot of our games we have played very well and created a host of chances. It's just our conversion rate has not been as good," said Brendan Rodgers, celebrating his first league win as Liverpool manager. "But today we were fantastic.
"This was another masterclass in finishing (from Suarez) ... it was a special day for him and the team."
Nuri Sahin and Steven Gerrard scored Liverpool's other goals.
Everton, which is a notoriously slow starter to league seasons, has won four of its opening six matches after Nikica Jelavic scored twice at Goodison Park to hand Southampton a fifth loss.
"I'd like to be in there in the mix during the season but I don't think Manchester United and Manchester City will be worried to see Everton there at this time of the year," Everton manager David Moyes said.
Peter Crouch, making his 500th league appearance, also scored a brace in Stoke's 2-0 win at home to Swansea, which has lost three in a row after its impressive start.
Sunderland beat 10-man Wigan 1-0 for a first win of the campaign, Steven Fletcher grabbing the winner soon after Jordi Gomez was sent off.
Demba Ba equalized twice for Newcastle in a 2-2 draw at Reading where all the goals came in an entertaining second half. Ba appeared to use his arm in scoring his second, which denied Reading a first victory since being promoted.
Terry shrugged off jeers from Arsenal fans to deliver a composed display for Chelsea and received a rapturous welcome from the jubilant travelling support after the match, slapping the badge on his jersey.
The centre back was available while he contemplates whether to appeal the suspension for making a racial slur at Queens Park Rangers defender Anton Ferdinand in a league match last year.
Terry lost Gervinho for Arsenal's equalizer in the 42nd but hardly put a foot wrong otherwise.
"It was the right choice to pick him today," Di Matteo said. "John showed his leadership qualities and what a good defender he is for the team."
The loss ended Arsenal's unbeaten start and saw the team's defensive vulnerability resurface, with centre back Laurent Koscielny at fault for both goals from Mata's set pieces.
"Defensively, we were just not at the level you have to be in a game like that, which is where we were punished today," Arsenal manager Arsene Wenger said.