Diego Costa and Oscar both scored twice before Andre Schuerrle completed Swansea's home humiliation to go provisionally five points ahead of Manchester City, which hosts Arsenal on Sunday.
United struggled through the first half at QPR before a second-half turnaround saw substitutes Marouane Fellaini and James Wilson clinch a 2-0 victory.
While United provisionally returned to third place — ahead of Southampton's late game at Newcastle — QPR remains in the relegation zone after a fifth straight league match without a win.
Tottenham moved up to fifth with a 2-1 victory over Sunderland, Liverpool won 2-0 at Aston Villa, bottom-place Leicester lost 1-0 to Stoke and Crystal Palace came from two goals down to beat Burnley 3-2, making it two wins out of two under Alan Pardew.
There were also five goals in south Wales but they were all scored by Chelsea — four in the opening 36 minutes. And the first came 49 seconds into the match, with Oscar's 20-yard (meter) shot.
Diego Costa added two more in the 20th and 34th, before Oscar grabbed a second for a 4-0 lead at halftime.
Substitute Schuerrle made it 5-0 in the 79th, three minutes after replacing Willian.
Jose Mourinho's side inflicted the worst home defeat in 24 years on Swansea, which sold top goalscorer Wilfried Bony to City midweek.
Gylfi Sigurdsson was dropped into a deeper role with Portuguese striker Nelson Oliveira handed his first start following his loan move from Benfica, but the formation did not seem to suit Sigurdsson as he gave away possession in the opening minute.
Oscar strode forward with purpose and lashed home a shot which flew past Lukasz Fabianski in the Swansea goal and was officially timed at 49 seconds.
Cesc Fabregas' 15th assist of the league season set up Diego Costa's first and the Spain striker then seized on poor defending to score his 17th goal of the campaign.
Costa's cut-back then allowed Oscar to net Chelsea's fourth with ease. The only surprise was it took Chelsea until the 79th minute to net again, with Schuerrle tapping Branislav Ivanovic's cross into an empty net.
By contrast, Man United has been struggling to score. Fellaini's opener at QPR — from Antonio Valencia's pass — was only the team's second goal in six hours of league action.
The second at Loftus Road came in stoppage time on the counterattack, when QPR was pushing for an equalizer, with Wilson netting from the rebound after first being denied by goalkeeper Robert Green.
At White Hart Lane, there was no debut goal from Sunderland striker Jermain Defoe against his former club. Defoe's transfer to Sunderland was announced Friday, part of a deal that sent U.S. international forward Jozy Altidore to Toronto FC of Major League Soccer.
Jan Vertonghen's second-minute opener for Tottenham was cancelled out by Sebastian Larsson's curled free kick but Christian Eriksen struck the hosts' winner in the 88th.
There was a fourth win in five games for seventh-place Liverpool. Fabio Borini volleyed in his first goal of the season before Rickie Lambert's low strike at Villa, which has gone nearly nine hours without scoring.