Denis Shapovalov and Felix Auger-Aliassime beat Russian duo Daniil Medvedev and Roman Safiullin 4-6 7-5 10-7 in the doubles to complete a tense 2-1 victory for Canada.
World No.14 Shapovalov edged Safiullin 6-4 5-7 6-4, but US Open champion Medvedev levelled up with a 6-4 6-0 win against Auger-Aliassime in the other singles match.
That set up a doubles showdown for the right to face Spain, who overcame Poland on Friday, which Canada came from behind to win.
Russia held in the opening set to take the lead, though a break of serve late in the second set for Canada ensured the contest would be decided by a tiebreak.
Shapovalov and Auger-Aliassime held their nerve at Ken Rosewall Arena, recovering from 6-5 down to win 10-7.
It marks a remarkable comeback in more ways than one for Canada, which lost its first four matches of the competition.
"Denis helped me and the team to push myself," Auger-Aliassime said in his on-court interview.
"We had a tough start in the doubles, so to be able to come back in this way, it's really a team effort.
"That's what the ATP Cup is about. You can still win after being one-all and losing a tough singles. It's really about the team effort and we're happy to be through."