The Blues emphatically ended their Everton hoodoo on Saturday evening 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.
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.
"Man United got an important point at Anfield but at least it makes us recover some points and get closer to second position."
Today's win maintained Villas-Boas' 100% home record since his summer appointment as Chelsea manager, the Portuguese making Stamford Bridge the fortress it was under former mentor Jose Mourinho.
"We have done nothing else than our responsibilities in winning the games that we have won at home," Villas-Boas said.
"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."
Chelsea went into tonight's game having not beaten Everton since the 2009 FA Cup final.
The Toffees were also undefeated on their previous five visits to Stamford Bridge and looked like making it six in the first half hour today.
But Juan Mata once again proved Chelsea's inspiration, the £23million man starting the move that saw Daniel Sturridge break the deadlock and also laying on the third goal for Ramires either side of a John Terry header.
Villas-Boas refused to single out Mata for special praise, saying: "It's all interrelated with his colleagues.
"The talent in this squad is so immense and the technical staff's job is just to free the players.
"When they play with freedom of choice, they can express themselves a little bit better."
Instead, Villas-Boas hailed the patience of his entire team.
"We managed to be very, very patient in our build-up, playing a lot from the back, tiring the strikers of Everton a little bit," he said.
"When Everton got the ball, they couldn't respond with the usual aggressiveness that they have.
"It was decisive to get the second goal just before half-time.
"The 3-0 gave us the comfort we needed to take the game through."
That third goal saw Ramires suffer a knee injury that makes him a doubt for Wednesday night's Champions League game with Genk.