Manchester City shrugged off the Carlos Tevez affair by brushing aside Blackburn Rovers, whilst United edged past Norwich and Newcastle won at Wolves. For the 20th time in a Merseyside derby a player saw red. This time it was Everton's Jack Rodwell who was controversially dismissed in the 2-0 defeat to Liverpool at Goodison Park.
Everton held out until the 71st minute when Andy Carroll scored, then Luis Suarez wrapped up the points with nine minutes remaining.
Liverpool could have been even more comfortable but Dirk Kuyt missed a penalty just before the break.
Manchester City scored four second-half goals to ease past struggling Blackburn as the Rovers fans made their views known at the final whistle increasing the pressure on boss Steve Kean.
Adam Johnson put City in front in the 56th minute, then four minutes later Mario Balotelli made it two.
Samir Nasri added a third before substitute Stefan Savic headed home his first for the club.
Manchester United showed Norwich a lesson in the art of finishing at the top level with a 2-0 win at Old Trafford.
The Canaries had their moments but failed to take them and United then scored two second-half strikes from Anderson and Danny Welbeck to remain top of the Premier League.
Sunderland looked on course for another home defeat as they conceded two goals in the opening five minutes against West Bromwich Albion but rallied to be level at the break and that's how it finished 2-2.
James Morrison and Shane Long looked to have set Albion on their way to a first ever top flight away win in October but Nicklas Bendtner scored his first goal for the Black Cats and the hosts were level by the half-hour as Ahmed Elmohamady restored parity.
Aston Villa maintained their unbeaten start to the campaign with a comfortable 2-0 home success over Wigan.
Gabriel Agbonlahor opened the scoring in the 36th minute and then turned provider for Darren Bent just after the hour mark.
Newcastle are now third in the Premier League following their best ever start to a season in 17 years after a 2-1 win over Wolves at Molineux.
Demba Ba headed home in the 17th minute and Jonas Gutierrez added a solo second in the 38th minute to make it 2-0 by the break.
Wolves were denied a penalty after what appeared to be a foul on Jamie O'Hara and, after Steven Fletcher pulled a goal back late-on, Kevin Doyle had a goal disallowed by a linesman.
