A superb Diego Costa strike stretched Chelsea's winning run to nine matches, equalling their streak from 2007, after they overcame West Brom 1-0 on Sunday in the Premier League.
Costa's 12th goal of the season sees the Blues maintain their three-point advantage over Arsenal who briefly went top on goal difference after beating Stoke 3-1 on Saturday.
It was a good day for the top two as others in the chasing pack dropped points.
Liverpool stay third -- six points off the top -- but for a second successive week dropped points when they were expected to win.
Defensive errors, just as in the 4-3 defeat by Bournemouth last Sunday, saw them held 2-2 at home by struggling West Ham.
The Gunners' north London rivals Spurs lost ground after going down 1-0 at Manchester United but despite the loss remain in fifth on 27 points, 10 adrift of Chelsea.
United, for whom Henrikh Mkhitaryan opened his account in the Premier League before going off on a stretcher with a left ankle injury, are 13 points shy of the leaders but only six off the Champions League spots.
United manager Jose Mourinho hailed the three points haul as "magic" and said he thought Mkhitaryan risked missing just two weeks.
West Brom made it difficult for Chelsea at Stamford Bridge until Costa seized on the ball 14 minutes from time, brushed off the attention of Gareth McAuley and rifled the ball past Ben Foster into the top far corner.
Chelsea manager Antonio Conte feted his players for winning nine in a row -- scoring 23 and conceding just two goals -- in a "very tough league".
"I'm very happy. We faced a tough, physical team. They're difficult to break down and we showed great patience to find the right solution," said the 47-year-old Italian.
The United and Spurs match was of a far better quality with the hosts going close through Paul Pogba, who hit the post and also forced Spurs' French goalkeeper Hugo Lloris into a superb save in the second-half.
The visitors could have gone home with a share of the points but for a woeful misdirected header from unmarked Kenyan midfield enforcer Victor Wanyama.
"Our heart was in our hands but the players gave us everything. These three points are magic because it's against a very good team so it means more for us," Mourinho told Sky Sports.
Liverpool made the dream start against the Hammers through Adam Lallana -- set up by Sadio Mane -- but the visitors showed the commitment they had been accused of lacking last week by manager Slaven Bilic in storming back to lead 2-1.
A free-kick by Dimitri Payet -- which underfire goalkeeper Loris Karius could have done better with -- and then a terrible misjudgement by Joel Matip allowed Michail Antonio to put them ahead.
However, another piece of trickery by Mane bamboozled the Hammers defence and a terrible error from his cross by Irish international 'keeper Darren Randolph allowed Divock Origi to level.
Feature image source: Reuters