Andre Villas-Boas' men arrived with a 2-0 advantage from the first leg of the last 16 tie and mainly focused on holding onto what they had in a disciplined defensive performance in Turin.
The hosts produced their share of eye-catching and inventive attacking play but largely struggled to craft clear openings, with Alexander Farnerud's set-piece deliveries their major threat.
And while Torino did score, Kamil Glik's header came in the final minute, not leaving enough time for a second, despite a stoppage-time rally from the hosts in which Fabio Quagliarella had an effort cleared off the line.
Zenit's aggregate win means that the Russian Premier League side are into the last eight of a European competition for the first time since they lifted the UEFA Cup in 2008.
Farnerud curled a 17th-minute free-kick agonisingly wide, by which time Zenit were already taking time out of the game at every opportunity.
Maxi Lopez had a chance to reduce the deficit a few moments later but the Argentine forward produced an ugly air shot.
A free-kick almost brought Torino back into the tie again when Quagliarella's rasping strike was deflected wide in the 36th minute.
Lopez was unable to turn home from the resulting corner and Quagliarella then sent a tame effort into goalkeeper Yuri Lodygin's arms when unmarked at the back post.
Axel Witsel was on target for Zenit in the first leg and Torino defender Emiliano Moretti made a fine block to stop the Belgian from increasing his team's advantage three minutes before the break.
A marginal offside call went against Torino captain Glik when he headed home a Farnerud set piece four minutes after the re-start, while Quagliarella had penalty appeals waved away following a challenge from Anatoliy Tymoshchuk as the match became increasingly fractious.
Lodygin could have few complaints when he finally earned a 58th-minute yellow card for time wasting.
But the keeper made a far more significant contribution 12 minutes from time with a brilliant double save to thwart Alessandro Gazzi before Glik's header sparked a grandstand finish.
Torino would fall gallantly short, with Quagliarella going closest when substitute Nicolas Lombaerts made a vital clearance as the forward steered goalwards.
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