Nicolas Gaitan and Talisca struck late as Benfica came from behind to beat Zenit 2-1 and clinch a Champions League quarter-final berth on Wednesday.
Zenit appeared to have done enough to overturn a 1-0 first-leg deficit and force extra time at the Petrovsky Stadium when Hulk headed in Yuri Zhirkov's cross in the second half.
However, with the clock winding down, Raul Jimenez tried his luck with an unlikely half-volley from long range that Yuri Lodygin could only parry and Gaitan was on hand to nod in the rebound.
That left Zenit needing two goals to progress and they were caught with a late sucker punch as Talisca drilled home a half-volley in injury time to earn a 3-1 aggregate win and spark jubilant Benfica celebrations.
It was tough on a Zenit side who had dominated the second half with Igor Smolnikov and Artyom Dzyuba wasting particularly good chances, but their wait to play in the Champions League last eight goes on.
For Rui Vitoria's Benfica it was another dramatic ending after Jonas' injury-time goal in the first leg gave them the advantage in the last-16 tie and they now join Wolfsburg and Real Madrid in the last eight.
Jonas almost doubled Benfica's lead early on when his bending 25-yard free-kick was athletically tipped over by Lodygin.
Zenit responded when Mauricio's long ball over the top was not dealt with and Dzyuba flashed a half-volley wide from the edge of the area when he perhaps should have hit the target.
The end-to-end nature of the contest continued and Benfica worked the ball well on the edge of the area before Renato Sanches drilled a low effort agonisingly wide of the left-hand post.
Benfica goalkeeper Ederson, making his Champions League debut, was then out quick to snuff out a route-one move that led to Dzyuba finding space in the area, while Hulk saw a 25-yard free-kick deflected wide.
Unsurprisingly, Zenit controlled possession in the second half, but initially failed to create chances.
Andre Villas-Boas - set to leave Zenit at the end of the season - introduced Oleg Shatov and Smolnikov on the hour and the latter wasted a gilt-edged opportunity.
Hulk picked out his team-mate with a cross from the right, but he failed to make clean contact in the six-yard box and Ederson made the simple save.
Moments later, Shatov burst into the box and laid off to Dzyuba, who could only shoot over the crossbar from 10 yards.
But the pressure finally told in the 69th minute. Zhirkov outmuscled Nelson Semedo and worked his way to the left of the area before hanging a perfect cross for Hulk to nod in and level the tie.
The visitors almost mustered an immediate response when Victor Lindelof's header was clawed out of the top corner by Lodygin.
Zenit hearts were broken in the 85th minute, though. Jimenez let fly with an audacious attempt that Lodygin palmed against the woodwork and Gaitan was on hand to gleefully head home into the unguarded goal.
Talisca's stoppage-time strike only served to rub salt in the wounds for Villas-Boas, whose dreams of making European history with Zenit crumbled around him.
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