Unfancied Southampton's first defeat since the opening day of the season allowed champions Manchester City to stay second, while neighbours Manchester United returned to the top four for the first time in more than a year by beating Everton 2-1.
Diego Costa scored his ninth goal in seven league games to tie up the points for Chelsea after Eden Hazard had converted a first-half penalty.
Costa's strike was set up by a perfect pass from Cesc Fabregas, the former Arsenal midfielder who joined from Barcelona in the close-season.
The victory extended Jose Mourinho's unbeaten record against Arsenal's Arsene Wenger to 12 meetings, the two managers being briefly involved in a spat on the touchline when Wenger pushed his opposite number in the chest.
"He was coming to my space," Mourinho said. "If it was to give an instruction to a player I say OK, but to press the referee to give a red card to an opponent is not fair.
"I don't think that is the image of Arsene Wenger as an advocate of fair play.
"It was an important match for both teams and these conditions make for a game of emotions."
Wenger said he was responding to a bad tackle, adding: "I went out of my technical area because I wasn't happy with the challenge and I wanted to see what happened.
"Someone stood in front of me and that was it. I say absolutely nothing else on that."
Christian Eriksen scored the only goal after 40 minutes as Tottenham won in the league for the first time since Aug. 24, giving manager Mauricio Pochettino a triumph over his former club and successor Ronald Koeman.
Eriksen's goal enabled Spurs to move up to sixth place.
They are level on points with fourth-placed Manchester United, who shot up six positions with an eventful success against Everton.
Goalkeeper David De Gea saved a penalty from Leighton Baines and earned the gratitude of manager Louis van Gaal with three more fine saves as Everton pressed hard at the end of a feisty affair.
Steven Naismith had equalised for Everton between goals by Argentina's Angel Di Maria and Colombia's Radamel Falcao -- his first for United.
Everton remained in the bottom four but stayed out of the relegation places when bottom club Queens Park Rangers were beaten 2-0 in the other London derby at West Ham United.
An early own goal by Nedum Onuoha was followed by a second half header from prolific Senegalese striker Diafra Sakho, sending the home side up nine places to seventh.
(Writing by Steve Tongue; editing by Toby Davis/Rex Gowar)
