In the buildup to the 2012 Games, Zverev took part in the 2011 IPC Athletics World Championships held in Christchurch. There he took the gold medal in his favoured 400m sprint, with a time of 49.41, a championship record. The following year he represented Russia at the 2012 Summer Paralympics in London. He qualified for two events, the 200m T13 and 400m T13 sprints. In the 200m sprint he qualified through his heat in first place, but missed out on a medal by 0.04 seconds, finishing in fourth place. In the 400m he qualified comfortably through the heats to reach the final. At the final, despite running a personal best of 48.83, he was beaten into the silver medal position by fellow countryman Alexey Labzin.