Justin Kripps, Ryan Sommer, Cameron Stones and Ben Coakwell defeated the Latvian team of Oskars Kibermanis, Lauris Kaufmanis, Arvis Vilkaste and Matiss Miknis by 0.13 seconds. on Sunday.
It was the Canadian quartet's first World Cup triumph since they recorded back-to-back wins at Lake Placid, USA at the start of the season.
Germany who have been dominant in the four-man competition had to settle for one podium place as Johannes Lochner, Florian Bauer, Christopher Weber and Tobias Scheider took third spot.
The German team led by Francesco Friedrich came fifth in Switzerland but he finished top of the World Cup standings with 1,686 points, beating Lochner and Kripps who came second and third respectively.