The draw means Zenit finish second in Group G on nine points, behind surprise-package APOEL Nicosia on their head-to-head record after the Cypriots lost 2-0 at home to Shakhtar Donetsk
Porto have to settle for a Europa League spot, ending third on eight points.
"We missed goals and more goals," said Porto coach Vitor Pereira. "We showed quality up front but lacked effectiveness and the passage of time favoured Zenit. We leave the Champions League with the feeling of deserving to qualify,"
Zenit, who came from behind to beat Porto 3-1 in Russia, looked to have a draw in mind as they kept their defensive shape despite Porto's strong start.
The hosts soon took control of midfield and fenced off Zenit's counter-attack threat thanks to hardworking midfielders Fernando and Joao Moutinho.
"We had chances and kept trying but they just parked the bus in the back," said a frustrated Kleber.
Hulk found space in the box and toe-poked the ball just wide of Malafeev's goal from a tight angle, while James and left-back Alvaro Pereira also missed excellent chances.
It still looked like a matter of time before Porto would find a way through but Malafeev was equal to everything they threw at him and Luciano Spalletti's side held on for a memorable qualification.
"This is a big disappointment, we should have gone through to the last 16, that was our ambition. We did all we could but things just did not go our way," said Moutinho.
