Chelsea are now within three points of the tied Manchester rivals, and the Blues boss aims to catch up with the leaders in the coming weeks.
"I'm very happy with such a performance before an international break and after all the positive results for our opponents on Saturday," Villas-Boas said after the match.
"Next game, two title contenders play each other - Liverpool and Manchester United. Then the two Manchester clubs play each other the week after that.
"It is important for us to continue to win and close the gap. We have a difficult game against Everton and then another difficult game with QPR.
"But, hopefully, if we manage to get six points out of those matches, it will put us in an even better position."
The five-goal romp saw two goals from Daniel Sturridge and a Frank Lampard hat-trick.