Blues down Gunners in derby

London - Chelsea went five points clear at the top of the Premier League after a 2-0 win at home to Arsenal in a fiery all-London clash on Sunday.

Eden Hazard gave Chelsea a 27th-minute lead with a coolly-taken penalty after he had been brought down in the box by Gunners defender Laurent Koscielny.

Diego Costa's ninth goal in seven Premier League games after an excellent lofted through-ball from former Arsenal favourite Cesc Fabregas sealed Chelsea's victory 12 minutes from time.

Kick-off at Stamford Bridge was delayed by 15 minutes as officials slowed the entry of Arsenal fans into the away end after a flare was set off.

There was a flare-up of a different kind when Arsenal manager Arsene Wenger clashed with Jose Mourinho on the touchline, the Frenchman pushing his Portuguese counterpart to one side before the feuding bosses were separated.

Chelsea then saw goalkeeper Thibaut Courtois leave the field with suspected concussion following a collision with Arsenal's Alexis Sanchez.

Victory saw Chelsea go five points clear of second-placed reigning champions Manchester City and meant Wenger was still left searching for his first win against a Blues side managed by Mourinho in what was his 12th attempt.

This defeat, Arsenal's first in the Premier League this season, left the Gunners nine points off top spot.

It also extended their miserable away record at their English title rivals, with the Gunners now having won six points from 21 league matches at the home grounds of top five clubs.

Earlier, Radamel Falcao's first goal for Manchester United secured a 2-1 victory over Everton.

Colombia striker Falcao -- signed on loan for a reported 10 million euros (7.8 million, $13.1 million) on transfer deadline day -- marked his fourth United appearance by scoring from inside the box after getting on the end of Angel di Maria's long-range shot in the 62nd minute.

Argentina midfielder di Maria had given Louis van Gaal's side a 27th-minute lead when he curled in a shot from just inside the penalty area after an excellent pass from Juan Mata.

Everton could have equalised on the stroke of half-time after they were awarded a penalty when Luke Shaw brought down Tony Hibbert.

But Leighton Baines's spot-kick was too close to David de Gea, who dived to his right to make a fine one-handed save -- the first of several fine stops.

However, Baines recovered his composure to whip in a superb cross from which Gary Naismith headed Everton level 10 minutes after the break.

Stoppage-time saw de Gea preserve United's lead with two impressive saves to deny Everton substitutes Leon Osman and Bryan Oviedo.

The result meant United had their first back-to-back successes under Dutch manager van Gaal following last week's 2-1 victory at home to West Ham.

"David de Gea was fantastic," van Gaal told the BBC.

"It was not easy for him because he had a lot of players in front of his view. Despite that he stopped good and speedy shots."

Turning to his new goalscorer, the manager said: "Falcao was forcing himself last week against West Ham. I told him to be satisfied about his performances and that the goals are coming. The goals are coming!"

Everton's defeat was compounded by John Stones being carried off on a stretcher late on -- placing a question mark over the defender's participation in England's upcoming Euro 2016 qualifiers with San Marino and Estonia.

"John Stones has an ankle ligament problem. It's too early to know the extent of it but it must be something serious for him to come off," said Everton manager Roberto Martinez.

Christian Eriksen's 40th-minute shot from the edge of the box was good enough to give Tottenham Hotspur a 1-0 win at home to high-flyers Southampton -- the club Spurs manager Mauricio Pochettino left before moving to White Hart Lane in pre-season.