United’s run of five consecutive league wins was brought to a halt in south Wales when Michu canceled out Patrice Evra’s opener for the visitors.
The game ended in acrimony, with United manager Alex Ferguson saying Swansea captain Ashley Williams “could have killed” striker Robin van Persie with a clearance.
United is four points ahead of Manchester City, while Chelsea returned to third place as seven different players scored for the rampant London team against Villa.
After Fernando Torres’s header in the third minute, David Luiz, Branislav Ivanovic, Frank Lampard, Ramires (twice), Oscar and Eden Hazard also scored.
The victory matched Chelsea’s record rout of Wigan in May 2010, and maintained the team’s revival since Rafa Benitez took charge last month.
“We are enjoying playing again and we needed that attitude to get us out of the sticky patch we were in,” Lampard said.
But Chelsea is seven points behind City and 11 adrift of United in its search for a first Premier League title since 2010.
United, though, could have been further ahead entering the packed fixture program over Christmas and New Year.
Evra put United ahead after 16 minutes in south Wales, glancing a header past Michel Vorm after latching onto Van Persie’s cross.
Although Jonathan de Guzman had an equalizer ruled out, Michu’s goal was given in the 29th, tapping into the net after David de Gea parried an initial attempt from De Guzman.
Tempers flared late in the game after Williams cleared the ball directly onto Van Persie’s head while the striker was on the ground. Van Persie squared up to Williams and both players were booked.
“The Van Persie situation you can clearly see that he could have been killed,” Ferguson said.
“He (Williams) should be banned for a long time because that was the most dangerous thing I’ve seen on a football field for many years. It was absolutely deliberate,” Ferguson added. “The whistle has gone, the game has stopped and he has done that right in front of the referee.”
The day’s other match was so one-sided that even with two penalties being awarded to Chelsea there was no hint of acrimony, with no one booked.
Chelsea was rampant from the start, with Torres taking just three minutes to meet fellow Spaniard Cesar Azpilicueta’s precise cross from the right flank with a header that beat goalkeeper Brad Guzan.
The striker has netted seven goals in his last six games, having netted only seven in the opening four months of the season.
Chelsea went further ahead on the half-hour when Luiz curled a free kick into the top corner and Ivanovic headed home four minutes later after Guzan parried Gary Cahill’s shot.
Chelsea’s fourth was a landmark goal for Lampard, who stabbed the ball into the net from distance to net his 130th topflight goal for the club, surpassing Bobby Tambling’s record set between 1959 and 1970.
“I’m very proud of that goals record, to beat a great man such as Bobby who is an absolute legend and a lovely bloke, it means everything,” said Lampard, who joined Chelsea from West Ham in 2001.
“Coming across London is not always easy but (the fans) have supported me.”
Lampard’s future, though, remains in doubt with the 34-year-old midfielder’s contract expiring at the end of the season. He has been linked with a move to the Los Angeles Galaxy.
“I love playing here,” he said. “I’m pleased to be fit and I will keep trying to enjoy my football. I believe I have a lot in me to go. I don’t want to get too deep. The club’s position is their position. I’m here to play football to show people what I can do.”
There were more goals to come.
Ramires scored his first in the 75th, putting the ball through Guzan’s legs after latching onto a cross from Lucas Piazon, who had just come on to make his league debut.
Oscar hit Chelsea’s sixth from the penalty spot four minutes later after being fouled by Chris Herd.
The seventh came in the 83rd when Hazard weaved through the hapless Villa defense and sent the ball into the top corner.
Although Piazon had a spotkick after being brought down, Ramires found time to net his second in stoppage time after being setup by Oscar.