Alexander Kerzhakov headed home a dramatic winner in the second minute of stoppage time, triggering wild celebrations in the Petrovsky Stadium.
Alexander Zernov gave Rotor an early lead, but Zenit captain Andrei Kobelev equalized after 21 minutes. Rotor was reduced to 10 men just before the interval when defender Sergei Rashevsky was sent off for a second yellow card.
Zenit piled on constant pressure in the second half but wasted numerous chances before Kerzhakov's strike.
The win gave Zenit 53 points from 28 matches, three points behind leader Spartak, which has a game in hand.
Spartak can clinch its sixth consecutive league title if it beats Zenit in Moscow on Saturday.
Saturn Ramenskoye hammered Alania Vladikavkaz 5-0, with five different goalscorers contributing. The win put Saturn on 47 points, two points behind third-placed Lokomotiv Moscow.
Torpedo Moscow beat lowly Fakel Voronezh 3-1 thanks to a first-half brace by Dmitry Vyazmikin.
On Saturday, Spartak defeated Anzhi Makhachkala to move a step closer to retaining its title.
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