Nuri Sahin and Steven Gerrard scored Liverpool's other goals.
Champions Manchester City, without a win in any competition for four games, came from behind to win 2-1 at Fulham with a late winner from substitute Edin Dzeko only a minute after coming on.
Everton maintained their good start to the campaign, coming from behind to beat Southampton 3-1 with all their three goals coming in 13 first-half minutes with Nikica Jelavic scoring twice.
In the other games, Stoke City won for the first time this season and sent Swansea City to a third successive defeat with Peter Crouch scoring both in their 2-0 win on his 500th league appearance.
Sunderland also won for the first time this season after four straight draws with Steven Fletcher, the only player to score for them in the league so far, grabbing the winner in their 1-0 win over Wigan Athletic who had Jordi Gomez sent off.
Reading were denied their first win after going 2-1 up against Newcastle United when Demba Ba appeared to secure the equaliser and his second goal in a 2-2 draw with his arm.
Reading climbed one place off the bottom to 19th while Queens Park Rangers, who play West Ham on Monday, slipped to last.