Russia led the pool coming into the decisive clash after a run of five straight victories, although it showed little ambition of making that six by beating Croatia for the first time in six meetings.
Seemingly happy instead to sit on a goalless draw that would keep it on course for Qatar, the visitor sought to rely on a defensive record that saw them concede just once in its winning run.
That approach looked to have paid off with the game entering the final 10 minutes and Croatia short of ideas, only for an inadvertent intervention from a Russia defender to turn the situation on its head.
A hopeful Croatia cross from the left skidded through a sodden penalty area and bounced off the knees of left-back Fedor Kudryashov, squirming beyond goalkeeper Matvey Safonov into the bottom-right corner.
Incredibly, that was the first goal in four matches between the sides in qualifying for the European Championship and World Cup.
Russia, who had attempted only one shot to Croatia's 19 up to that point, suddenly scrambled forward in search of an equaliser, but the 2018 finalists clung on, condemning their opponents – hosts of the last finals – to the play-offs.