Everton’s win at West Brom earlier on Thursday – achieved by the same margin – had Carlo Ancelotti’s side temporarily in the Champions League spots. Additionally, Tottenham had beaten Fulham by an identical scoreline to put the pressure on.
Mason Mount, though, settled the affair with a goal shortly before half-time, putting Chelsea on 47 points, one clear of the Toffees.
Liverpool, who have lost five home matches in succession for the first time in top-flight history, remain static on 43.
Manchester City had extended their lead at the summit to 15 points with a hard-fought victory over Wolves on Tuesday evening.
But their neighbours were unable to close that gap to 12 as they played out a frustrating stalemate at Selhurst Park 24 hours later.
Nemanja Matic came closest to breaking the deadlock with a deflected effort in the first half, but the Red Devils were unable to find the breakthrough despite dominating possession throughout.
To the Foxes' credit, they came from behind to earn their point, with Kelechi Iheanacho's wonderful volley cancelling out an early Matej Vydra strike.
But neither side could claim all three points, despite Ashley Westwood and Youri Tielemans both striking the post in the second period.
Elsewhere, Sheffield United kept their slim hopes of avoiding relegation alive as they beat Europe-chasing Aston Villa 1-0.
David McGoldrick scored the crucial goal for the Blades, who held out despite Phil Jagielka's dismissal on the hour mark.
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