Zubkov drove the Russian sled to the fastest time in both runs and his combined time of 1:32.5 gave him a lead of .32 of a second over the Swiss sled driven by Beat Hefti.
American Steven Holcomb was third, just .04 of a second out of a silver medal position.
Holcomb and another U.S. driver, Cory Butner, held down the second and third spots after the first run, but the Swiss sled had a quick trip down the course in the second attempt to move up.
The U.S. sled piloted by Cory Butner fell from second place to the No. 11 position. Butner had only the 16th quickest trip in the second run.
Holcomb won the Olympic four-man bobsled gold medal in Vancouver and is trying to capture the first two-man medal for the United States since 1948.
The final two runs will take place Monday.