Torino had kept their opponents comfortably at bay for the first half an hour of Thursday's meeting at the Stadion Petrovsky, but Benassi's sending-off for two bookable offences gave Zenit a huge boost.
Managed by Andre Villas-Boas, winner of this competition in 2011 with Porto, Zenit took full advantage of Benassi's red card to take a significant step towards the quarter-finals.
The home side took the lead when Axel Witsel - the man fouled by Benassi for his second yellow - applied a close-range finish in the 38th minute.
Witsel was the beneficiary of a kind rebound, and it was a similar story for Domenico Criscito's second after the interval when Hulk's shot off the post ran perfectly into his path.
Victory continued Zenit's fine form since they returned from their mid-season break, with Villas-Boas' men now having recorded four consecutive wins in all competitions without conceding.
Salomon Rondon, who scored a hat-trick in Zenit's 3-0 win over Ural at the weekend, saw a shot kept out by the legs of goalkeeper Daniele Padelli in the third minute.
Zenit had the better of the opening exchanges, with Torino content to sit back and try to frustrate their opponents.
But their job was made much more difficult when Benassi - earlier cautioned for a cynical foul on Hulk - was shown a second yellow card shortly before the half-hour for a high challenge on Witsel.
Seven minutes before half-time, Zenit capitalised on their numerical advantage to open the scoring.
Witsel was the man to break the deadlock, converting a rebound after Padelli had parried Igor Smolnikov's initial effort back into the danger zone.
Zenit thought they had doubled their lead five minutes later when Rondon tucked home, but the striker's effort was ruled out for a marginal offside call.
The home side continued to dominate after the interval, and Padelli's right foot kept out Hulk's effort following good link-up play with Danny.
Hulk and Danny combined to great effect again in the 53rd minute and when the former's shot came back off the upright, Criscito - formerly of Torino's city rivals Juventus - was on hand to slot the ball into the empty net.
The remainder of the game proved largely uneventful, and Torino - unbeaten in their six home matches in this season's competition - will be tasked with turning around a two-goal deficit in next week's return leg.
