Finalists at the closing World Cup in 2018, Croatia seemed bound for the play-offs for plenty of Sunday's recreation, as they toiled on a waterlogged pitch towards a resolute Russian defence.
But Kudryashov's error noticed them grab pinnacle spot from the visitors eight mins from time and secure their passage to next 12 months's match in Qatar.
An early header from Andrej Kramaric set the tone for a primary half in which Croatia had the lion's share of possession and piled on the stress looking for an opener.
Marcelo Brozovic also shaved the bar with a long-variety effort, before both he and Josip Juranovic pressured saves from Russian keeper Matvey Safonov.
Safonov beat away every other Kramaric header with a reflex keep just after the break, before denying substitute Bruno Petkovic at the hour mark.
The conditions made it tougher and tougher for Croatia as the second 1/2 advanced, with the pitch becoming ever greater boggy below the heavy rain.
The possibilities had all but dried up when Borna Sosa despatched a hopeful ball into the field on 82 mins.
Though underneath no pressure, Kudryashov struggled to manipulate the ball as it skidded on the moist floor, and watched helplessly on as it bounced off his knee and inside the put up.
While Croatia qualify automatically as Group H winners, Russia can nevertheless make it thru through the play-offs.
