The St Petersburg side hosted second-placed CSKA Moscow at the Petrovsky Stadium on Sunday and triumphed 2-1 thanks to a double from star striker Hulk.
Consequently, Zenit are now on the verge of a first title since 2012, as they are now eight points clear of the defending champions with just nine games remaining.
Villas-Boas, though, is urging everyone associated with the club to keep their feet firmly planted on the ground.
"We cannot relax," the Portuguese told reporters. "Everything is very open and I don't believe that CSKA have stopped dreaming about the championship."
Zenit, of course, are still in contention to win the Europa League and will face Sevilla in the quarter-finals later this month.
As a result, Villas-Boas added that he intends to make full use of his squad in the coming weeks, while insisting the league remains his priority.
"If we rotate, we do that for injuries or because of suspension," the 37-year-old coach added.
"We do that to keep everyone in top shape. It's possible that we will make changes but my view is to make sure we win the league and do everything that we can for that."
Villas-Boas is bidding to win his first trophy since leading Porto to a treble in 2011, having been sacked in his two previous jobs with Chelsea and Tottenham.