Liverpool came through a tough Premier League test at Crystal Palace on Saturday with a 2-1 win at Selhurst Park.
Manchester City beat Chelsea 2-1 after coming from behind at the Etihad Stadium, with the champions climbing to third.
Jose Mourinho enjoyed victory during his first match in charge of Tottenham Hotspur, winning 3-2 at West Ham United.
A 96th-minute equaliser by Alexandre Lacazette rescued Arsenal after a 2-2 draw at home to Southampton.
Leicester's fine run gained more energy with a 2-0 away victory at Brighton & Hove Albion, and Everton continued to misfire after losing 2-0 against Norwich City at Goodison Park.