A late own goal by Fedor Kudryashov secured Croatia’s place at next year’s World Cup in Qatar and left Russia in the play-offs.
A draw would have been enough for Russia to finish top of Group H and they looked to be on course to achieve that with neither side able to find a breakthrough.
But Kudryashov bundled a cross into his own net with eight minutes to go.
Victory means Croatia finish top with 23 points, one point ahead of Russia.
Vyacheslav Karavayev had the chance to snatch the draw the visitors needed in the 90th minute but he shot just over the crossbar.
