Luis Suarez scored the only goal against QPR as a dominant Liverpool avoided a fifth successive home draw and climbed to sixth in the table.
Clint Dempsey's late winner helped Fulham end 10-man Liverpool's hopes of a seventh away win in a row.
Second half goals from Rodriguez and Kelly gave Liverpool a comfortable win over Chelsea at Stamford Bridge.
Joleon Lescott's own goal cancelled out Vincent Kompany's effort as 10-man Manchester City restored their five-point lead at the top of the Premier League.
Glen Johnson grabbed a late winner as Liverpool beat Chelsea in a fluctuating game at Stamford Bridge.
A late wonder save from keeper Michel Vorm earned Swansea City a memorable Premier League point as Liverpool extended their unbeaten home record.
Charlie Adam and Andy Carroll were on the scoresheet as Liverpool extended their run of unbeaten games to seven after a comfortable win over West Brom.
Luis Suarez capped a superb individual display with a late winner as Liverpool came from behind to beat Stoke in the Carling Cup fourth round.
Grant Holt came off the bench to rescue a point for Norwich against a wasteful Liverpool at Anfield.
Substitute Javier Hernandez earned Manchester United a point after England striker Wayne Rooney was left out of the starting line-up at Anfield.
Watch English Premier League match, Everton Vs Liverpool highlights here.
Venue: Goodison Park.
Date: Saturday, 1 October.
Kick-off: 1245 BST.
Liverpool resisted a second-half fightback from Wolves to secure a hard-fought victory in the Premier League.
Liverpool captain Steven Gerrard made his comeback after six months on the sidelines as they came through a potentially hazardous Carling Cup third round tie at Brighton unscathed.
Nine-man Liverpool were embarrassed at White Hart Lane as Tottenham cruised to a 4-0 win.
Stoke ended Liverpool's unbeaten start to the season thanks to Jonathan Walters' first-half penalty.
Jordan Henderson and Charlie Adam scored their first goals for Liverpool as they went top of the Premier League with a deserved victory over Bolton.
Liverpool cruised into the third round of the Carling Cup with a one-sided win over League One outfit Exeter.
Liverpool struck twice late on to secure their first league win at Arsenal for 11 years and increase Arsene Wenger's troubles.
Sebastian Larsson scored a superb volley on his debut to earn a point for Sunderland at Liverpool.
Watch friendly football match, Liverpool Vs Valencia highlights here.