Toby Alderweireld deflected a right-wing cross towards the net in the 74th minute and Belgian Courtois, on loan from Chelsea, flapped at the ball as it dropped over his head and into the net for a precious equaliser for the Russians.
Zenit are second in the table with six points from five matches, two more than Porto ahead of the Portuguese team's tussle with bottom club Austria Vienna later on Tuesday.
Leaders Atletico (13 points), who were already through to the knockout stage as group winners, went ahead in the 53rd minute when Adrian Lopez raced clear on the left before slipping the ball under keeper Yuri Lodygin.
(Editing by Tony Jimenez)
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