With the win, Canada moves into a tie for second place in the 12-team round-robin standings with Germany's Johnny Jahr. The undefeated Thomas Ulsrud of Norway (4-0) has sole possession of first place.
"We played better and the ice was better," said Koe. "We had a bit more confidence out there, and we played pretty good. We didn't have to talk so much about weight.
"Yesterday, honestly, spots were 10 to 15 feet different from each other. Today, it was a couple feet max, and that makes it a lot easier on the brains."
Koe's rink opened the tournament Saturday with a 6-3 win over Denmark. But dropped a 9-6 decision to Japan Sunday before beating host China 9-6.
The Canadians were scored at 96 per cent collectively against Russia, with lead Nolan Thiessen and second Carter Rycroft both scoring perfect games.
"That felt way better," said Rycroft. "We threw some stinkers yesterday, and we were lucky to get away with 1-1. Finally, today, we felt like we got a bit of a handle on things.
"We were throwing them properly. Still missing a few, but at least we're throwing them with conviction. The results? You can't worry about them too much because you still get caught on certain spots."
Canada stole single points in each of the first four ends. Russia scored a point in the sixth, though it missed an opportunity for a potential deuce.
The game was put away in the seventh as the Russians' attempt at a steal went south, and Koe scored five to prompt handshakes.
"We're happy to be 3-1," said Koe. "Obviously, we would have liked to have that (loss to Japan) back yesterday when we were up three. But that's going to happen every once in a while. Three-and-one, that's not a bad spot."
Canada plays Jiri Snitil of the Czech Republic later Monday.