After Wolves missed several chances in the first half, Raul Jimenez pounced in the 61st minute to break the deadlock with his second goal of the season.
Frank Lampard scored his 200th goal for Chelsea who beat West Ham United 2-0 to move into third place in the Premier League above Tottenham Hotspur who suffered a shock 1-0 home defeat by Fulham on Sunday.
Holders Chelsea will face Premier League opposition in the third round of the FA Cup after Sunday's draw gave them a tricky start to their defence away to Southampton.
Images from the English Premier League matches played on Saturday.
Arsenal stayed top of the Premier League after two goals in five minutes from Spain international midfielder Santi Cazorla set them on their way to a 2-0 win over Fulham who remain mired deep in the relegation battle.
Manchester United manager David Moyes has suffered a stuttering start to life at Old Trafford but it could have been far worse for the Scot if he had failed to retain the services of striker Wayne Rooney.
United have struggled this season, collecting 10 points from their opening seven Premier League matches and being dumped out of the League Cup by second-tier Derby County.
Chelsea's terrible start to the season plumbed new depths on Saturday when the Premier League champions lost 2-1 at West Ham United.
Steven Gerrard scored two penalties as Liverpool went back to the top of the Premier League with a 2-1 win at West Ham United to complete a Merseyside win-double over London clubs on Sunday. Whereas in Bundesliga Sascha Moelders brought an end of the unbeaten run of Bayern Munich.
Arsenal's best chance to equalise came from a Granit Xhaka free kick which looked destined for the top corner until the Gunner's former keeper Emiliano Martinez at full stretch pushed it around the post with a fingertip save.
News of all that's transpired on and off the football field
Tottenham Hotspur manager Harry Redknapp has criticised Wayne Rooney after the Manchester United striker was charged with using foul language while celebrating a goal in Saturday's 4-2 win at West Ham United.
Nuno's coaching staff have also been relieved of their duties. The club have not yet announced a replacement but British media reported former Chelsea and Inter Milan boss Antonio Conte is linked.
Saturday's clash between Manchester United and Tottenham Hotspur at Old Trafford is already shaping up as an early-season eliminator to challenge runaway leaders Manchester City for the Premier League title.
Manchester United will sign Argentine Carlos Tevez for a British transfer record fee of 32 million pounds.
Chelsea take on Hull City in the opening match of the English Premier League on Saturday, August 15, at 1715 IST.
Goals rained in for Manchester City and Manchester United but Juergen Klopp's first game in charge of Liverpool was solid rather than spectacular with his new side drawing 0-0 at Tottenham Hotspur in the Premier League on Saturday.
Samir Nasri has left Manchester City for Sevilla on a season-long loan, the Premier League club announced on Wednesday. Like goalkeeper Joe Hart, who joined Torino on loan earlier, the former French international midfielder does not feature in new manager Pep Guardiola's plans.
England goalkeeper Robert Green received stinging criticism at home on Sunday following an horrendous mistake which cost his side victory in their opening World Cup game against the United States on Saturday. Millions of fans watching at home and in pubs across the country held their heads in their hands as West Ham United keeper Green let Clint Dempsey's weak shot slip through his fingers in Rustenburg.
Ole Gunnar Solskjaer believes the club's old guard will face real competition after manager Alex Ferguson's spending spree.
Former Manchester City manager John Bond has died at the age of 79, the Premier League club said on Wednesday.
Manchester United's Romelu Lukaku does not consider himself a complete striker but is optimistic of creating his "own history" at Old Trafford.
Chelsea will have a massive void to fill in midfield next season after the club's all-time record goalscorer Frank Lampard announced on Monday he was ending his 13-year spell at Stamford Bridge.
A summary of Saturday's action in the English Premier League.
England have cancelled Wednesday's international soccer friendly with the Netherlands at Wembley on police advice as forces focus on dealing with rioting and looting in the capital.
Images from the English Premier League matches played on Sunday
Chelsea will be fined 25,000 pounds ($38,327) and asked for their observations on three disciplinary incidents that occurred in Saturday's eventful 2-1 defeat at London rivals West Ham United.
Images from the English Premier League match between Arsenal and West Ham United on Tuesday.
Steven Gerrard scored two penalties as Liverpool went back to the top of the Premier League with a 2-1 win at West Ham United to complete a Merseyside win-double over London clubs on Sunday.
IMAGES from the English Premier League matches played on Saturday
Manchester United have accepted Wayne Rooney's charge from the FA for swearing at a TV camera, but are appealing against his two-match ban, the Football Association said on Tuesday.
The English Football Association charged Nicolas Anelka on Tuesday for making a 'quenelle' salute after scoring for West Bromwich Albion against West Ham United in the Premier League last month.
A late Emmerson Boyce own goal gave Champions League-chasing Tottenham Hotspur a 2-2 draw at lowly Wigan Athletic which did little to help either side at opposite ends of the Premier league table on Saturday.
Southampton returned to the Premier League after a seven year absence when they beat Coventry City 4-0 on Saturday to clinch second place in the Championship (second division) and take the remaining automatic promotion spot.
Sunderland entrusted flamboyant Italian Paolo Di Canio with the task of securing their Premier League survival when they appointed him as head coach in place of the sacked Martin O'Neill on Sunday.
IMAGES from the English Premier League matches played on Sunday.
Ivory Coast midfielder Yaya Toure landed his third successive African Footballer of the Year award on Thursday to cap a memorable week.
Liverpool climbed to the top of the Premier League table with a 2-1 victory over struggling Wolverhampton Wanderers on Saturday.
France midfielder Paul Pogba is to undergo a medical at Manchester United ahead of a transfer from Serie A champions Juventus, the English Premier League club said on Sunday. United have been widely reported as being prepared to pay a world record fee of 120 million euros (101.78 million) for the 23-year-old who joined Juventus on a free transfer from the Old Trafford club in 2012. "Paul Pogba has been granted permission to have a medical in order to finalise his transfer from Juventus to Manchester United," said the statement.
Tottenham Hotspur flop David Bentley rejoined former club Blackburn Rovers on loan on Friday and Manchester City's Dutch teenager Karim Rekik has also moved to the English second tier side on a short-term deal.
