Holcomb, from Park City, Utah, and push athlete Steve Langton of Melrose, Massachusetts, had a two-run time of 1 minute, 45.26 seconds. Rush, teaming with Lascelles Brown, followed in 1:45.30.
"I didn't win by much in this race," Holcomb said. "Lyndon is on his home track, and it's not easy to beat him here. I knew I had to lay down a smoker to keep the lead. ... I hope I can carry this momentum to Europe. We'll be in the Germans' backyard, and they'll play rough."
Germany's Francesco Friedrich was third in 1:45.60.
In the women's race, Canada's Kaillie Humphries pushed her winning streak to six.
Humphries and rookie brakeman Chelsea Valois had a two-run time of 1:48.68. Switzerland's Fabienne Meyer and Elisabeth Graf were second in 1:49.37, and Germany's Sandra Kiriasis and Brett Wiacker third in 1:49.50.
"North America seems to like me and I like it," Humphries said. "Hopefully, we can keep this streak alive as we head over to Europe. I know we have some big challenges ahead."
Humphries' streak started in Whistler last February, the track where she won an Olympic gold medal in 2010.