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.
