Calgary's Alex Gough and Sam Edney and doubles tandem of Justin Snith of Calgary and Tristan Walker of Cochrane, Alta., raced to a combined time of two minutes 14.129 seconds.
"It was enjoyable to get on the podium in Latvia after having the Latvian team snuff us one year ago at the Olympics for that bronze medal," said Edney. "Our team needed this result overall. It hasn't come as easy to us this year as it has in the past. It's clear to us other nations have caught up and are set on raising the bar so winning a bronze medal on a track like Sigulda means a lot to our entire team, and we are thrilled to bring it home for Canada."
The Canadians were heavy favourites for a medal when the team relay made its debut at the 2014 Olympic Winter Games in Sochi. They finished a heart-breaking fourth.
The bronze-medal performance didn't come without controversy. Officials questioned whether Edney touched the green finishing pad at the end of the track. After video replay it was confirmed Edney did hit the pad.
Germany won the relay in 2:13.152, while Russia claimed the silver at 2:13.234. The relay consists of one women's, one men's and one doubles sled. Athletes hit a pad hanging over the track after crossing the finish line, which opens the start gate for the next team member.
Edney was 17th in his singles earlier in the day, and drew motivation from his disappointing finish.
"My second run earlier in the day in singles race got affected by some wind on the start and I lost my opportunity at a top-10," Edney said. "I tried to bottle up that energy for the team relay. Alex had a solid run time, and I had a fantastic run so I was happy."