Zenit were knocked out of the Champions League on Tuesday after a 3-0 away defeat to Benfica, who secured a Europa League spot.
Benfica clinched the victory thanks to Franco Cervi's tap-in, Pizzi's penalty and an own goal from Sardar Azmoun as Zenit played over a third of the match with 10 men following Douglas Santos' dismissal.
Zenit finished bottom of the group as Lyon fought back from two goals down to draw 2-2 against RB Leipzig and ended up a point ahead of them in Group G.
Benfica claimed the Europa League spot courtesy of a better head-to-head record with the Russian side with both teams level on seven points.
Zenit appeared prepared to bide their time in the first half as the action unfolded in Lyon.
Benfica left-back Alex Grimaldo struck a free-kick straight at Zenit goalkeeper Mikhail Kerzhakov but it was the only shot on target by either side in the first half.
Iran forward Azmoun looked Zenit's most likely source of a goal before the break and he sent two efforts from long-range wide.
The game sparked into life when Benfica took the lead two minutes into the second half through Cervi.
Benfica midfielder Pizzi found space down the left flank and his low cross picked out winger Cervi, who tapped in from close range.
Zenit suffered the double blow of a penalty and a man sent off just before the hour mark when the ball was harshly deemed to have struck the hand of Douglas, the defender then shown a second yellow card.
Pizzi confidently buried the spot-kick as he sent Kerzhakov the wrong way and things went from bad to worse for Zenit when Azmoun deflected a corner into his own net with 11 minutes left.
Zenit's misery was complete when news filtered through of Lyon's late equaliser against Leipzig.
What does it mean? Zenit out, Benfica into Europa League
A lacklustre display by Zenit saw the consolation of even a place in the Europa League slip from their grasp as they finished bottom of Group G.
Benfica's emphatic victory ensured they will be playing continental football in February, with Leipzig and Lyon finishing as group winners and runners-up respectively.
Energetic Pizzi catches the eye
Benfica needed their experienced players to step up on a tense night and Pizzi delivered. The 30-year-old was a bundle of energy and creativity, scoring one goal and assisting another with one of his four key passes.
He has now has scored in three of his last four Champions League games for Benfica, having failed to score in any of his first 33 appearances in the competition.
Night to forget for Ivanovic
At 35 Branislav Ivanovic is in the twilight of his career and the former Chelsea centre-back's legs were creaking at the Estadio da Luz. The Serbia defender was not the commanding presence of old as Benfica over ran Zenit's defence in the second half.
Key Opta Stats: One of Zenit's worst Champions League losses
- Zenit suffered their joint-heaviest defeat in the Champions League, and largest since losing 4-1 against Austria Vienna in December 2013.
- This was Benfica's joint-biggest win in the Champions League, also beating Celtic 3-0 at home in November 2006.
- Zenit mustered just three shots in this match, with their only attempt on target coming in the 77th minute.
- Cervi scored his first Champions League goal in 19 games since netting against Dynamo Kiev in October 2016.
- Douglas became the first Zenit player to be sent off in the Champions League since Domenico Criscito in February 2016, which also came against Benfica.
Benfica return to domestic action as they look to consolidate their lead at the top of the table when they host third-placed Famalicao on Saturday.
Zenit have just started their mid-season winter break in the Russian Premier League so will have plenty of time to contemplate this loss with their next match more than two months away.