Manchester City dislodged Liverpool with the win even though both have 62 points.
But Manchester City have the upper hand on goal difference, having played one game more than Juergen Klopp’s side.
It is the first time Manchester City have been top since Dec. 8.
Liverpool will now face Bournemouth on Saturday, while Manchester City host Chelsea a day later.
The match was a re-arranged fixture caused by Manchester City’s advance to the League Cup final.
The visitors took the lead on the stroke of halftime when French defender Aymeric Laporte was left unattended to head home a David Silva free kick curled in from the left.
The goal was the 17th conceded by Everton from a set-piece in all competitions this season.
Two of Manchester City’s substitutes combined for the second goal deep in stoppage time with Kevin De Bruyne playing Gabriel Jesus in on goal.
Although the Brazilian’s shot was blocked by Everton goalkeeper Jordan Pickford, he reacted quickly to head home the loose ball.