Jurgen Klopp vowed Liverpool will be a "pain in the backside" in the race for the Champions League places.
Table-topping Arsenal bounced back from conceding Said Benrahma’s opening goal to secure a 3-1 home win over West Ham which moved them seven points clear in the Premier League.
Liverpool held off Aston Villa's plucky challenge to close the gap on the Premier League's top four.
Newcastle showed they can be part of the Premier League title race, moving second in the table with a 3-0 win at Leicester.
New Wolves manager Julen Lopetegui marked his Premier League debut with a dramatic late 2-1 victory at Goodison Park which ramped up the pressure on Everton boss Frank Lampard.
Antonio Conte hailed Harry Kane for sparking Tottenham's latest fightback against Brentford after they slipped behind yet again in the Premier League.