Bacary Sagna and Cesc Fabregas were Arsenal’s scorers at Goodison Park, with Tim Cahill’s 89th-minute consolation coming too late for Everton.
Arsenal are now just two points behind Chelsea, with third-place Manchester United – who drew 2-2 at Aston Villa on Saturday – a further point behind. Manchester City are fourth, six points behind the leaders, after drawing at home to Birmingham on Saturday.
Chelsea’s makeshift defence, which was missing first-choice centre backs John Terry and Alex, was ripped apart by Sunderland’s lively attacking display, and manager Carlo Ancelotti acknowledged Sunderland were worthy winners.
“Everything went wrong,” Ancelotti said. “We didn’t play well or how we wanted. Sunderland played with fantastic spirit, fantastic pressure.
“It was a bad day. We were not able to play our football, just 15 minutes in the first half. Everything was difficult today, it was a strange performance.”
It was Chelsea’s heaviest home defeat since April 2002 and their second loss in three league matches, having been beaten 2-0 at Liverpool last Sunday.
Since going down to an embarrassing 5-1 defeat at northeast neighbour Newcastle on Oct. 31, Sunderland have picked up seven points from a possible nine to move up to sixth place.
“Two weeks ago, we were hung, drawn and quartered,” Sunderland manager Steve Bruce said. “We were looking for a response and got it. They have worked very hard to get over the Newcastle defeat.
“It was the worst performance of my career two weeks ago and today was arguably the best.”
Paulo Ferreira, usually a right back, was played out of position in central defence alongside Branislav Ivanovic for Chelsea, and the pair were all at sea.
Onuoha opened the scoring in the last minute of the first half when he waltzed around two defenders before slipping a left-footed shot past Petr Cech for his first goal for Sunderland.
Gyan took advantage of more holes in the Chelsea defence by making it 2-0 in the 52nd, finishing off a flowing move involving Boudewijn Zenden, Welbeck and Jordan Henderson by curling his finish around Cech.
Chelsea did not seriously threaten Sunderland goalkeeper Craig Gordon and conceded a third, in the 86th, when Welbeck pounced on Ashley Cole’s wayward back pass and guided a low finish past the stranded Cech.
Arsenal have bounced back from a 1-0 home defeat to Newcastle last Sunday by winning two straight away games, the victory at Everton following a 2-0 success at Wolverhampton Wanderers on Wednesday.
“We’ve had two difficult away games but we have got six points and that puts us in a good situation. The team has shown great spirit,” Arsenal manager Arsene Wenger said.
Sagna scored a rare goal when the France right back smashed a shot into the roof of the net at the near post in the 36th.
Fabregas doubled Arsenal’s lead three minutes into the second half after exchanging passes with Marouane Chamakh before steering a low shot into the far corner.
Everton piled the pressure on in the final 20 minutes but found goalkeeper Lukasz Fabianski in inspired form.
Cahill managed to find a way past the Poland international in the 89th when the Australia international bundled in from close range after Louis Saha had headed down a corner at the far post.
“I can’t really feel as if we deserved an awful lot. I don’t think we played all that well,” Everton manager David Moyes said. “I didn’t think Arsenal were great and I don’t think we were.”
Earlier, Nemanja Vidic preserved Manchester United’s unbeaten start to the season with a late equaliser on Saturday at Aston Villa, while Gareth Bale’s double against Blackburn helped Tottenham end a four-match winless streak.
Vidic’s 85th-minute header secured a 2-2 draw for United at Villa, four minutes after Federico Macheda’s powerful strike started the fight-back for the 18-time champions.
United had also conceded twice in four minutes, with Ashley Young scoring from the penalty spot and Marc Albrighton netting from close range in the 76th.
“We came back well but it was too late and we shouldn’t have been in that position,” United manager Alex Ferguson said. “Our passing was poor. Normally we can control the match. We didn’t control it.”
Spurs had no such problems against Blackburn, coasting to a 4-2 victory that puts them three points behind fourth-place Manchester City, who slumped to its second successive 0-0 draw at home to Birmingham.
Bolton are a place below City, with Stuart Holden’s first league goal clinching a 3-2 win at Wolverhampton.
Wolves are only being kept off the bottom by West Ham, who were held to a 0-0 draw by Blackpool. Newcastle’s home match with Fulham also finished 0-0, while Wigan beat West Bromwich 1-0.