The London side cut through their opponents' defence at will in the first half at the Reebok Stadium, with Lampard and Daniel Sturridge - who scored eight times in 12 games during a loan spell with Wanderers last season - both netting twice.
Sturridge headed the visitors in front in the second minute, teed up Lampard in the 15th and Chelsea then raced into a 4-0 lead with less than half an hour of the contest gone, two errors in quick succession by home goalkeeper Adam Bogdan allowing the Blues pair another goal each.
Back with a bang: Frank Lampard has scored four goals in two games
Dedryck Boyata pulled one back for Bolton a minute into the second half, but it counted for little as Lampard completed his treble just before the hour mark to wrap up a thumping win.
Villas-Boas - appointed as Chelsea boss in the summer - said afterwards that he thought the result, the most impressive of his tenure so far, was the kind his team's attacking play has warranted for some time.
His sentiments were echoed by Lampard, who believes the side are progressing well with the Portuguese at the helm.
Steady progress: Lampard believes Chelsea have improved under Andre Villas-Boas
'We are trying to show what we are about in training and when a new manager comes in, sometimes it can take time for his effect on the training ground to carry over onto the pitch,' Lampard said.
'There were a lot of times when we had some okay performances early in the season - Manchester United, Valencia, for example - and we have played a lot of games where we have created a lot of chances and not finished them off, which takes the gloss off a result sometimes.
'I think there have been a lot of signs of our developing understanding in recent games but Bolton was the day where we put it together as the finished article.
Hat-trick hero: Lampard picks up the match ball after the game
'Everything happened for us from the start. You saw the brand of football that we played - the passing and movement and quality throughout the team - and that is what we are working towards.
'We moved the ball and passed the ball and passed the team to death. On top of that, we have created a lot of chances and taken them. We need to keep doing that.'
The victory was Chelsea's fifth in seven Barclays Premier League games this season and saw them back up to third in the table, three points away from pacesetters Manchester United and Manchester City.
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