The former Porto manager had admitted before the Stamford Bridge clash that the Russian had asked for an explanation following Tuesday night’s 3-1 loss at Napoli in the Champions League.
Villas-Boas had named Frank Lampard, Ashley Cole and Michael Essien as substitutes for that game – and all three started against Bolton, who remain in the relegation places.
Lampard scored the third goal after David Luiz and Didier Drogba’s second-half goals had put Chelsea in control.
Villas-Boas attempted to laugh off suggestions that Abramovich had told him to bring back the three experienced campaigners, who were all trophy-winning mainstays under previous managers, including Jose Mourinho.
“I got the call this morning,” he joked before adding: “I’m not in tune with Roman’s agenda. All I know is that it was important for the team to win, mostly for the fans as they have been deserving and demanding a lot.
“At least they can go home smiling.”
The victory lifted pressure off Villas-Boas’s shoulders as a defeat would have intensified speculation that he might be sacked.
“The pressure has been on the team to get results,” he admitted. “Our form had not been good and we wanted to get back to winning ways.
“The most important thing is to build on this, solve the FA Cup tie and solve the Champions League tie and improve our position in the league.
“It is an important day because it can be a start and for it to be a start we have to get this form right.”
The next batch of games include an FA Cup replay at Birmingham City and the second leg of the Napoli clash but Villas-Boas refused to confirm whether Lampard would now be an automatic pick for all of them.
“It’s not the way it works,” Villas-Boas insisted. “He has been performing magnificently for the team but the others have been competent as well.
“There are six players competing for those three positions. And with a number 10 it is is competing for two. Whatever we do is for the benefit of the team.
“Lamps had his chance and played magnificently. It was normal squad rotation, nothing new.”
Bolton manager Owen Coyle was pleased with the way his side nullified Chelsea’s attack in the first half but was disappointed to fall behind two minutes into the second half, when Luiz scored.
“My disappointment is in the goals we give away,” he said. “The first we had good possession and David Luiz stepped into the play. He had a very kind break in the box when it came back to him but it was an exquisite finish.
“We were chasing the game and had one or two chances but the second one from the corner, we had a designated marker yet allowed a free header.
“We are disappointed by aspects of the second half.”
Coyle also backed Villas-Boas to be a success at Chelsea.
“There is no doubt he is talented,” the Scot said. “And he will come through the other side.”