The Blues emphatically ended their Everton hoodoo with a 3-1 win at Stamford Bridge, taking full advantage of United's lunchtime draw at Liverpool and staying within three points of new leaders Manchester City. The goals came from Daniel Sturridge, John Terry and Ramires, with Apostolos Vellios providing the consolation.
Next Sunday's Manchester derby will give Chelsea another chance to close the gap at the top, providing they win their own match at QPR.
Villas-Boas said: "It's important for us to get three points, particularly on a day where two title contenders played against each other.
"We have done nothing else than our responsibilities in winning the games that we have won at home. We have not done anything special.
"We just have to continue to win until we find a position of comfort at the top of the Premier League, because that's what we want."