Manchester City beat United in derby while Arsenal, Liverpool, Spurs all win

Pep Guardiola condemned Jose Mourinho to his first defeat as Manchester United manager as Manchester City emerged 2-1 winners from a pulsating, end-to-end derby encounter.

Kevin De Bruyne was the catalyst for the visitors, coolly opening the scoring after nipping past Daley Blind before firing a shot that hit the post and rebounded kindly for Kelechi Iheanacho to deservedly extend City's lead.

Mourinho's side, by contrast, were struggling until debutant goalkeeper Claudio Bravo's composure disappeared with his clean sheet, flapping at a Wayne Rooney free kick as Zlatan Ibrahimovic fired home with aplomb before the break.

Joe Hart's replacement looked flustered and was fortunate not to give away a penalty or collect a card soon after the restart, turning into danger and lunging at Wayne Rooney in the box.

A United equaliser was ruled out as substitute Marcus Rashford's strike deflected home off the offside Ibrahimovic, and De Bruyne hit the post at the other end as City held on for an important victory on enemy turf.

Arsenal took their opportunity to close in on the pacesetters at the top of the Premier League, but only just, edging to a 2-1 win against Southampton thanks to Santi Cazorla's late penalty at Emirates Stadium.

With the match deep into added time and both sides looking like taking a share of the spoils, Cazorla thrashed home a spot-kick to seal the points after substitute Olivier Giroud had been tugged to the ground by Jose Fonte.

But questions will be asked as to whether play should have been stopped by referee Robert Madley as Gunners' skipper Laurent Koscielny lay prone in front of the Saints goal with a head injury at the time.

Southampton had led through an own goal from Petr Cech with birthday boy Koscielny drawing Arsene Wenger's side level with a stunning overhead kick.

Roberto Firmino scored twice as Liverpool eased to a 4-1 win over Leicester City.

Liverpool took the lead after 13 minutes when James Milner slid a pass into Firmino on the edge of the box, and the Brazilian skipped past defenders before slotting his shot inside the near post.

Sadio Mane doubled Liverpool's advantage after the half-hour mark after Daniel Sturridge received a long pass over the top and laid the ball off for his overlapping teammate to score.

The defending champions pulled a goal back a few minutes later when defender Lucas Leiva took a poor touch in his own box and compounded the error by passing the ball into the centre for a waiting Jamie Vardy.

Lallana struck a hard shot into the roof of the net 11 minutes after half-time to put the game out of Leicester's reach, before Firmino capped the scoring in the 89th minute with a goal into an empty net.

Tottenham repeated their April annihilation of Stoke with another 4-0 win at the bet365 Stadium to maintain their unbeaten start to the season.

Spurs had only won once since thrashing the Potters at this venue five months ago when they looked like champions-elect and this was a performance in the manner of both that day and their late-season run.

Son Heung-Min, brought in for Erik Lamela after he played for Argentina in midweek, scored with two first-time finishes either side of the interval and England internationals Dele Alli and Harry Kane, both of whom scored doubles back in April, then found the net for the first time this season.

It was Kane's first in 10 games for club and country and his 50th Premier League goal in 87 top-flight appearances as he reached a welcome landmark ahead of the start of Spurs' Champions League campaign next week.

Defeat for Stoke ensured they remain rooted to the foot of the table and manager Mark Hughes had an elevated view for the second-half destruction having been sent to the stands by referee Anthony Taylor before the break.

Watford completed a remarkable comeback aided by poor defending from West Ham after firing four unanswered goals in a thrilling 4-2 Premier League victory.

Dimitri Payet twice set up Michail Antonio to give the Hammers a comfortable lead, only for Walter Mazzarri's men to spring into action on an afternoon of high drama at London Stadium.

Odion Ighalo, Troy Deeney, Etienne Capoue and Jose Holebas were on target as the home defence fell apart and, but for a little more accuracy in the final 10 minutes, Watford could have won by more.

Wilfried Zaha's opportunist strike handed Crystal Palace a first Premier League win of the season as they ended Middlesbrough's unbeaten start to the campaign with a 2-1 victory.

Zaha capitalised on a dreadful error by Boro full-back George Friend two minutes into the second half to clinch a deserved victory -- just a third in 23 league games in 2016 for manager Alan Pardew -- in front of a crowd of 30,551 at the Riverside Stadium.

Christian Benteke had earlier paid off the first instalment of his £27.5 million transfer fee by heading the visitors into a 16th-minute lead, his opening goal for the club, and although Boro defender Daniel Ayala levelled seven minutes before the break, Pardew's men were not to be denied despite two late penalty claims.

Jack Wilshere made his Bournemouth debut from the bench and promptly helped them to a first victory of the season against West Bromwich Albion.

The midfielder, who moved to the Cherries in a shock deadline day loan switch from Arsenal, came on after 63 minutes with the score goalless and his new team tiring.

And with 11 minutes remaining, a cheeky flick from Callum Wilson secured a 1-0 win for the hosts and a winning start for Wilshere.

Robert Snodgrass grabbed an injury-time lifeline for Hull City as they continued to show their fighting spirit with a 1-1 draw at Burnley.

Snodgrass, who grabbed a hat-trick for Scotland against Malta, again showed his eye for goal by bending a last-chance free-kick past Tom Heaton to cancel out Steven Defour's wonderful opener.

The Belgium international looked to have settled things in the home side's favour in the 73rd minute with an elegant solo run and shot but the Tigers, under caretaker boss Mike Phelan, continue to defy expectations this term.