In the first of the double header menu, Argentina had a comfortable 39-3 win over the United States.
"I didn't think we played a lot or rugby in the first half," said Canadian coach Kieran Crowley."But I think we put Uruguay under a lot of pressure.
Canada had the game won at halftime, leading 18-3 and then salting it away in the second half with a try and penalty goal.
Connor Braid led the Canadians with three penalty goals and two converts. Team captain Tyler Ardon, Patrick Parfrey and Liam Underhill all scored tries.
Uruguay's lone try came late in the second half from Juan Diego Ormaechea, with Felipe Berchesi converting. Berchesi also scored a game opening penalty goal four minutes into the game.
Canada twice was forced to play with just 14 players.
Tempers flared nine minutes into the second half when centre Nick Blevins was handed a 10-minute yellow card for a rough tackle on Uruguay's Gaston Mieres and then again at the 25 minute mark when Ardron was sent off for repeated infringement.
"In the second half we played better but you can't play well when you lose two players like we did," said Crowley. "But we did get the win which was good and now we have to look forward to Tuesday and the U.S."
Argentina, the two-time ARC defending champion, will be looking for a second straight win after soundly defeating the U.S. 39-3 in the tournament opening match.