* Chelsea win thrilling encounter against Everton 6-3
* Champions Manchester City stunned at home by Stoke
* Di Maria makes United debut in 0-0 draw at Burnley
* Swansea beat West Brom to maintain perfect start
By Toby Davis
LONDON, Aug 30 (Reuters) - It was a day of role reversal as Jose Mourinho's often cautious Chelsea thumped Everton 6-3 in a thriller on Saturday while champions Manchester City's attacking talents were blunted in a shock 1-0 home defeat by Stoke City.
New signing Diego Costa was on target twice, scoring for the third Premier League game in a row, as Chelsea produced a swashbuckling performance to overwhelm Everton at Goodison Park.
"It was wonderful for everyone at the stadium and people watching television around the world but not for me," Mourinho told the BBC. "We cannot make so many defensive mistakes.
"We want to improve as a team by keeping our defensive strength and quality and improving in other areas. Today we showed we are improving in other areas but not keeping the balance in defence."
Manchester City dropped their first points of the season when Mame Biram Diouf scored a superb individual goal to silence the home fans who have become used to seeing one-sided romps at the Etihad Stadium.
It was also another miserable day for Manchester United, their frustrations continuing after a 0-0 draw at promoted Burnley with British record signing Angel Di Maria unable to spark an improvement in their fortunes.
Swansea City's excellent start to the season continued as they swept aside West Bromwich Albion 3-0 and they are level on a maximum nine points with Chelsea at the top of the fledgling table.
Southampton came from behind to beat West Ham United 3-1 while Crystal Palace, playing their first game under new manager Neil Warnock, scored through on-loan Wilfried Zaha in the fifth minute of stoppage time to grab a 3-3 draw at Newcastle United.
Queens Park Rangers beat Sunderland 1-0 to collect their first win since gaining promotion while the goals flowed for west London rivals Chelsea in a dynamic display by the normally pragmatic and defensively-sound Blues.
Everton were caught cold as Costa put the visitors ahead after 35 seconds and Branislav Ivanovic scored two minutes later, incensing the hosts who felt he had strayed offside.
The home side hit back seconds before halftime when Kevin Mirallas powered a header past keeper Thibaut Courtois but a Seamus Coleman own goal, after an excellent dribble by Eden Hazard, restored Chelsea's cushion.
It then had the feel of a basketball match as Steven Naismith's effort gave Everton hope before Nemanja Matic replied with his first goal for Chelsea.
Samuel Eto'o scored on his debut for the hosts, against his
former club, only to see Ramires and Costa complete the rout for the visitors.
Games at Manchester City have frequently resembled carefully scripted affairs with their glittering array of footballers showering the supporters with goals and entertainment.
Both were in short supply against a rugged and resilient Stoke who scored 13 minutes into the second half when Senegal international Diouf raced 60 metres before beating keeper Joe Hart.
It was only the second time in 71 games that Manchester City, who were ruthless in Monday's 3-1 win over Liverpool, had failed to score at home and it ended a run of seven consecutive league wins stretching back to last season's title triumph.
"It's a surprising defeat because we don't expect to lose against Stoke but these games sometimes happen," said manager Manuel Pellegrini.
"We were not very creative, we did not find the spaces and that is credit to Stoke."
There was more gloom for manager Louis van Gaal as Manchester United, who were embarrassed 4-0 in the League Cup by third tier MK Dons on Tuesday, again looked uncomfortable with their new three centre back system against Burnley.
With cameras panning to former boss Alex Ferguson yawning in the stands, questions are already being asked of Van Gaal who is struggling to implement his playing style and scrambling to recruit players before the transfer window shuts on Monday.
"The progress is there," the Dutchman told BT Sport, "but ... a club like Manchester United has to win. We have two points from nine and that's disappointing."
Di Maria, signed from Real Madrid for 59.7 million pounds ($99 million) on Tuesday, showed encouraging flashes in a 70-minute debut but United generally looked short of attacking ideas.
The Argentina winger was United's most dangerous player in the first half and the architect of their best chance with a searching long ball that found Robin van Persie who could not beat Burnley keeper Tom Heaton.
Swansea, who had beaten Manchester United and Burnley in their opening two games, completed a comfortable win over West Brom.
Nathan Dyer rounded the keeper and slotted the ball into an empty net after two minutes before Wayne Routledge volleyed home beautifully midway through the first half.
Dyer then stroked home a Gylfi Sigurdsson pass to complete the scoring for Swansea.
Newcastle thought they had suppressed a spirited Palace when Mike Williamson put them 3-2 ahead in the 88th minute but Zaha, returning from Manchester United for a second spell at the club, levelled at the end.
West Ham paraded loan signing Alex Song before kickoff and took the lead against Southampton when Mark Noble struck with a deflected shot after 27 minutes.
Morgan Schneiderlin then scored twice for Saints and Graziano Pelle added a third to hand manager Ronald Koeman his first Premier League win. (Editing by Tony Jimenez)