Oscar and Diego Costa each scored twice as Chelsea established a provisional five-point lead at the Premier League summit with a crushing 5-0 success at Swansea City on Saturday.

The one-sided victory, which saw Chelsea go 4-0 up inside the first 36 minutes, enabled Jose Mourinho’s side to pull clear of second-place Manchester City, who host Arsenal on Sunday.

Wins for Southampton, Manchester United, Tottenham Hotspur and Liverpool meant that there was little material change in the race for the Champions League places, although Arsenal slipped to sixth.

Chelsea had lost two and won only one of their previous four away games, but they went ahead inside a minute at Swansea, with Oscar drilling a shot into the bottom-left corner after Gylfi Sigurdsson conceded possession.

Eager to atone, Sigurdsson hit the crossbar within seconds of the restart, but Chelsea doubled their lead in the 20th minute when Cesc Fabregas teed up Costa to slot home.

Costa punished a mistake from Federico Fernandez to claim his 17th goal of the campaign in the 34th minute and two minutes later he teed up Oscar to finish with the inside of his right foot.

A dominant first-half showing also saw Willian hit the woodwork twice, and although Chelsea took their foot off the pedal after the change of ends, Andre Schuerrle added a late fifth from Branislav Ivanovic’s cross.

“It was a perfect performance. The way everything went our way was just perfect,” Mourinho said.

“However, I keep saying that if you play fantastically well, but don’t win cups, in 20 years time nobody will remember you. Yes, we are playing well, but we have to win competitions.”

On-loan striker Radamel Falcao returned to the Manchester United starting XI at second-bottom Queens Park Rangers, but spurned a good early chance to score when he was denied by a Rob Green double-save.

United manager Louis van Gaal persisted with a three-man defence and with the visitors toiling, their fans made their dissent plain at half-time by chanting: “4-4-2!”

Van Gaal introduced Marouane Fellaini and 19-year-old striker James Wilson early in the second half, tweaking United’s shape, and within seconds the visitors were in front.

Antonio Valencia motored to the byline on the right and cut the ball back for Fellaini, who took a touch before languidly shooting past Green from 12 yards.

Wilson completed a 2-0 victory in injury time, finishing at the second attempt after his initial shot was repelled by Green.

“When I changed the shape, I wanted speed or pace also in the attacking line,” Van Gaal told MUTV. “It’s a change in attack that brings a lot of risk, but we have won 2-0 and I think it was deserved.”

United, briefly, moved up to third place, but Southampton reclaimed their spot on the podium by winning 2-1 at Newcastle United in the late game, which left Ronald Koeman’s side five points below City.

On-loan Dutch winger Eljero Elia was the match-winner, netting either side of a fortuitous equaliser by Yoan Gouffran, who scored when Florin Gardos’s attempted clearance struck him on the thigh and flew into the net.

Christian Eriksen claimed an 88th-minute winner as Tottenham Hotspur leapfrogged Arsenal into fifth place by winning 2-1 at home to Sunderland, who gave striker Jermain Defoe a debut against his former club.

Sebastian Larsson appeared to have earned Sunderland a point with a curling free-kick after Jan Vertonghen’s deflected shot had put Spurs ahead, only for Eriksen to poach a winner from Andros Townsend’s cross.

Improving Liverpool climbed to seventh, five points below the Champions League places, after winning 2-0 at Aston Villa.

With Steven Gerrard rested, Liverpool took a 24th-minute lead when Fabio Borini slid in to convert Jordan Henderson’s delicate cross before Rickie Lambert added a second with 11 minutes to play.

Crystal Palace continue to benefit from the impact of new manager Alan Pardew, coming from two goals down to claim a stirring 3-2 win at fellow relegation contenders Burnley.

Efforts from Ben Mee and Danny Ings put Burnley 2-0 up after 16 minutes, but Palace drew level through goals from Dwight Gayle and Jason Puncheon before Gayle netted an 87th-minute winner.

Victory sent Palace four points clear of the relegation zone and left Burnley one place above the bottom three.

Bottom club Leicester City remain three points adrift of safety after Bojan Krkic’s 63rd-minute strike earned Stoke City a 1-0 win at the King Power Stadium.