It was Italy's first victory in a men's relay since 1993.
But despite taking over with a 43.6 second lead from Italy in the final leg, Volkov picked up three penalties with the rifle as the Russian team slipped to second.
There was no such trouble for Lukas Hofer however for Italy as he incurred just one penalty to win the gold by 6.1 seconds, with Sweden collecting bronze.
Italy improved dramatically from their first World Cup relay finish of 12th and move up to fourth overall, just two points behind Sweden in third.
Despite missing out on victory Russia leapfrog Norway, who could only manage fifth in Germany, into first place and lead the World Cup on 108 points, eight ahead of the Norwegians.