With this victory against one of his rivals for the title, on the twelfth day, the Liverpool get eight points to Leicester and Chelsea, second and third classified, and nine to own Mancheser City, fourth.
Two goals in the first quarter of an hour, scored by Brazil's Fabinho (6) and Egyptian Mohamed Salah (13), and one by Senegalese Sadio Mane in the second half (51), allowed Liverpool to get their eleventh victory in twelve games , having tied the other.
The City complained of two hands in the area of his right side Trent Alexander Arnold, one of them in the play that preceded the first goal and the second in the last minutes.
Fabinho opened the scoring with a nice goal from outside the area, after a play driven in counterattack by Senegalese Sadio Mane.
City players claimed the referee for a previous hand within the Arnold area.
The second goal was born in another counterattack and a center of Andrew Robertson on the left, which topped Salah head to the net.
The City had no other solution but to attack, being the 'Kun' Aguero the player who carried more danger, although the clearest chance of the Manchester team came with a shot from the Spanish side Angelino to one of the clubs in the 29th minute.
But it would be Sadio Mane who would increase the advantage for Liverpool in the second half, by finishing off with a head from near a center from the right of Jordan Henderson.
With the game decided, Manchester City achieved both the honor, through the Portuguese Bernardo Silva (78). AFP