Zenit captain Danny struck the only goal of Wednesday's game late on after a contest low on quality at the Stadion Petrovsky.
Victory moved Zenit up to second in Group C ahead of Bayer Leverkusen's clash with Monaco later on matchday five.
"Our objective is to continue in the competition so the win was important," said Villas-Boas. "Now we will look for a result in Monaco - we must believe.
"The only time we did not have control of the possession was in the first 10-15 minutes of the second half.
"In the rest of the game we had the initiative. Benfica defended well but fortunately we managed to get the goal to give us three points."
Hulk set up the late winner with a neat clipped cross, but the striker dismissed any notion that his past with Benfica's fierce rivals Porto made him more determined.
The Brazilian added: "We needed back-to-back victories to move to the next phase. Thank God we managed to score and win the game.
"It is special to win any game, regardless of the opponent.
"I played for four years in Porto and our biggest rivals were Benfica.
"But I always had respect for the club, I don't hate Benfica."
