Chelsea's defensive lapses remain a problem, and Southampton punished their main weakness in a six-goal thriller at Stamford Bridge.
Former Paris Saint-Germain forward Edinson Cavani has joined Manchester United, who also announced two other deals on transfer deadline day.
Penggempur Everton, Theo Walcott, telah menjalani pembedahan perut dan bakal terlepas sambungan Liga Perdana Inggeris musim ini.
Theo Walcott will miss around four weeks of action for Everton having had surgery before the Premier League's return.
Mohamed Salah scored twice as runaway leaders Liverpool cruised past Southampton, while Everton came back from 2-0 down to beat Watford.
Frank Lampard left Olivier Giroud out of Chelsea's matchday squad to face Everton, who named Theo Walcott in their starting XI.
Manchester City boss Pep Guardiola hailed the "outstanding" display from his players to pick up three points at Everton on Saturday.
Christian Eriksen scored Tottenham's equaliser at home to Everton, though Spurs never looked in danger of losing their top-four spot.
Manchester United were embarrassed by a rampant Everton at Goodison Park as their top-four chances were dealt a significant blow.
Harry Kane and Son Heung-min starred in a remarkable and breathless 6-2 Tottenham win at Everton on Sunday.