Former Tottenham and Chelsea boss Villas-Boas formally replaced Luciano Spalletti last week after Zenit were eliminated from the Champions League by Borussia Dortmund, and led his new side into action on Monday looking to help them secure a first Premier League win since before the winter break.
Second-placed Zenit started 2014 in disappointing fashion with one point from their opening two matches - combined with their European exit - but they were celebrating a victory on Monday that brought them back to within three points of leaders Lokomotiv Moscow.
Hulk, who scored in last week's ultimately futile 2-1 second-leg win in Dortmund, put Zenit ahead from the penalty spot in the fifth minute and a Sergey Veremko own goal doubled their lead just after half-time.
However, Krylya quickly pulled a goal back through Ibrahim Tsallagov, and the visitors should really have got something out of the game only for striker Luis Caballero to see both of his spot-kicks saved by Lodigin in the 59th and 68th minutes.
In Monday's other match, fifth-placed CSKA Moscow beat rock-bottom Anzhi Makhachkala 3-0 away from home, Seydou Doumbia netting a brace in either half before Ahmed Musa wrapped up the win with a third goal 15 minutes from time.