Raheem Sterling's hat-trick helped Manchester City stay atop the Premier League on Saturday as Juergen Klopp picked up a point at Spurs in his first game as Liverpool manager. Wilfried Bony added two goals as City routed Bourne mouth 5-1 to remain two points clear of Arsenal and Manchester United. Sterling completed his hat-trick before half-time and Bony scored each side of the break to give City 11 goals in the past two games. Klopp's much-anticipated Liverpool debut ended in a hard-fought 0-0 draw at Tottenham There were few chances with Liverpool's Divock Origi hitting the crossbar and Spurs' Harry Kane twice denied by keeper Simon Mignolet. Chelsea avoided a second straight home loss with a 2-0 win over Aston Villa. Diego Costa gave Chelsea the lead and Alan Hutton's own-goal sealed just the third win of the season for the champions, who move up five places to 11th. Manuel Lanzini and Dimitri Payet scored late as West Ham beat 10-man Crystal Palace 3-1 to move up to fourth. Dwight Gayle was sent off with the score 1-1 just before half-time for a second yellow card. Palace were able to hold out until Lanzini scored with two minutes remaining and Payet added a goal in stoppage time. Jamie Vardy's brace earned Leicester City a come-from-behind 2-2 draw at Southampton. Jose Fonte and Virgil van Dijk gave the hosts the lead before Vardy hit back after the break to push his league-leading total to nine goals. Saido Berahino scored the only goal as West Brom spoiled Sam Allardyce's debut as manager of winless Sunderland.