Everton delivered an early blow to Chelsea's title hopes as they won 1-0 at Goodison Park, while Arsenal went top with victory over Sunderland and Manchester United beat ten-man Crystal Palace at Old Trafford.
Elsewhere, Tottenham cruised to victory over Norwich, Manchester City were held to a frustrating draw by Stoke -- and their former City boss Mark Hughes -- Newcastle recorded a second successive league win, at Aston Villa, Fulham drew with West Brom and Cardiff earned a point at Hull.
Jose Mourinho suffered the first Premier League defeat of his second spell as Chelsea manager as Steven Naismith's first-half goal gave Everton a 1-0 victory at Goodison Park.
The goal came against the run of play near the end of the first half, with Naismith heading home from close range, but the hosts were deserving of the three points by the end of a keenly-fought encounter.
Two goals from Aaron Ramsey helped Arsenal to a 3-1 victory in a topsy-turvy encounter against Sunderland at the Stadium of Light.
With debutant Mesut Ozil pulling the strings, the visitors dominated the first half, only for Sunderland to pull level and have two goals disallowed -- including one by Jozy Altidore -- in between Ramsey's double in the second half.
The win puts Arsenal level on points with Tottenham and Liverpool, with the latter, who have a game in hand, facing Swansea on Monday night.
David Moyes earned his first Old Trafford win as a first-half Robin van Persie penalty and a late Wayne Rooney goal helped Manchester United to see off ten-man Crystal Palace 2-0.
Palace had kept things tight until Kagisho Dikgacoi was red-carded after he was viewed to have brought down Ashley Young -- earlier booked for simulation -- inside the area. The decision was controversial, but Van Persie made no mistake in giving United the advantage just before the break.
Ian Holloway’s men kept the hosts at bay until the 81st minute, when Rooney, returning to action after missing the international break with a head wound, fired in a fine free-kick to complete the victory.
Gyfli Sigurdsson scored a brace as Tottenham secured a comfortable 2-0 win over Norwich at White Hart Lane.
New Spurs signing Christian Eriksen slotted a perfect through ball for Sigurdsson’s opener, a shot curled past John Ruddy from 15 yards.
Sigurdsson made sure of the win shortly after the break when finishing Paulinho's cross from five yards out; again, the superb Eriksen proved influential in the move.
Stoke spoiled Manuel Pellegrini's 60th birthday weekend as they claimed a 0-0 draw against Manchester City at the Britannia Stadium.
Former City boss Mark Hughes was left the happier, with neither side able find the winning touch.
City took time to settle and were reduced to long range efforts as Alvaro Negredo curled one over from 25 yards. At the other end, Stoke grew in confidence as Kenwyne Jones capitalised on a Samir Nasri mistake. However, Joe Hart was equal to the shot and spared Nasri's blushes.
New Stoke signing Marko Arnautovic almost netted on his debut, but his deflected shot was again well saved by Hart before Robert Huth was left out cold after suffering a knee to the head when challenging for a header with Negredo.
Both sides continued to probe for a late winner, but the home side did more than enough to earn a share of the spoils.
Aston Villa were subjected to boos at the final whistle after Newcastle came away from Villa Park with a 2-1 win.
Hatem Ben Arfa opened the scoring after Papiss Cisse had failed to connect with Loic Remy's pull back, leaving the Frenchman able to slot home.
Gabriel Agbonlahor might have equalised, but it was Christian Benteke who got them on level terms, rising to head home his fifth goal of the season.
However, the celebrations did not last long as, once again, the lively Ben Arfa left his men behind and fired a shot at goal. Brad Guzan pushed it into the path of substitute Yoan Gouffran, who sidefooted the ball home to give Alan Pardew a second successive Premier League win.
Fulham and West Brom played out an entertaining 1-1 draw at Craven Cottage.
Fulham took the lead when West Brom failed to clear a corner -- a weak header found its way to Steve Sidwell, who did not need a second invitation to commemorate his 400th senior appearance by firing in at the near post.
Fulham thought they had doubled their lead when Dimitar Berbatov had the ball in the net, but the goal was rightly flagged offside and they were punished when Gareth McAuley headed an equaliser at the death.
Cardiff continued their solid start to the season with 1-1 draw with Hull City at the KC Stadium.
The Tigers drew first blood when Tom Huddlestone sent a cleared corner back into the box and Curtis Davies was on hand to head home.
Cardiff responded after the break and had the ball in the net on the hour mark as a wonderful move was capped when Peter Whittingham volleyed in at the far post to equalise. Aron Gunnarsson almost stole the points for the away side late on, but his header bounced the wrong side of the post.