Chelsea counted on two-goal Alvaro Morata for their 3-1 win over Crystal Palace.
Morata's first-half strike was cancelled out by Andros Townsend as Chelsea struggled to subdue their vibrant visitors, for whom Wilfried Zaha starred.
But Eden Hazard, back from a three-game absence with a back problem, provided the striker's second with his first touch, sending over a free-kick which Morata expertly diverted into the net.
Blues boss Maurizio Sarri stated: "I'm really very proud but I'm proud to be coach of this team. The record is not the record of the coach but the team. I was lucky because I have very good players and in the last two months they were able to win without a great level of organisation from the tactical point of view.
"At the beginning we knew there was a gap of 30 points from last season. At the moment we need only to think about trying to recover a large part of the gap. I hope to recover almost all of it but I don't know. It's difficult to recover 30 points but we are trying."