Chelsea equalled the Premier League record for the most consecutive wins in a season despite conceding twice for the first time since September.
The Blues tied Arsenal's mark of 13 matches from 2001/02 with a 4-2 victory over Stoke at Stamford Bridge.
The Potters provided Antonio Conte's men with one of their toughest tests and Bruno Martins Indi cancelled out Gary Cahill's opener just after half-time.
Willian put Chelsea back in front but Peter Crouch netted his first Premier League goal in two seasons to equalise in the 64th minute.
However, parity lasted just a minute before Willian netted again, and Diego Costa made sure with a fourth in the 85th minute for the league leaders.
Chelsea now stand one win away from matching Arsenal's 14-match winning run, which ran from February to August 2002, spanning two seasons.
Manchester United scored twice in the final five minutes to turn the tables and beat Middlesbrough 2-1 at Old Trafford.
United, who had a first-half effort from Zlatan Ibrahimovic controversially ruled out, were stunned in the 67th minute when Grant Leadbitter put Boro ahead.
But Anthony Martial broke Boro's resistance in the 85th minute and a minute later Paul Pogba scored the winner.
A change in the hotseat made no difference to Swansea's fortunes.
Alan Curtis has taken temporary charge following Bob Bradley's sacking but Benik Afobe and Ryan Fraser scored in the first half and Josh King netted late on to give Bournemouth a 3-0 victory at the Liberty Stadium.
Champions Leicester won just their second Premier League match since October, 1-0 against West Ham.
In an end-to-end game, it was a surprise there was only one goal, scored by Islam Slimani in the 20th minute.
Andre Gray became the first Burnley player to score a hat-trick in the Premier League as the Clarets put more distance between themselves and the bottom three with a 4-1 victory over Sunderland.
Gray, who scored the winner against Middlesbrough on St Stephen's Day, put Burnley ahead in the 31st minute and then added two in three minutes shortly after half-time.
Ashley Barnes made it four from the penalty spot and Jermain Defoe's strike did nothing to brighten Sunderland's afternoon.
West Brom leapfrogged Southampton into eighth place in the table after coming from behind to win 2-1 at St Mary's.
Republic of Ireland striker Shane Long opened the scoring in the 41st minute but Matt Phillips equalised two minutes later and Hal Robson-Kanu scored the winner five minutes after the break.
It was the Welshman's first goal since his stunner against Belgium in the European Championship finals in the summer, and Southampton's afternoon had a sour ending when sought-after defender Virgil van Dijk was sent off.