The 29-year-old from Calgary put together two solid pushes with two consistent runs to clock a bronze-medal time of two minutes 17.32 seconds on the 1,700-metre non-refrigerated track.
"I'm really excited to get my first podium in St. Moritz. I had an excellent day today," said Fairbairn. "I don't think I expected it but I'm also not surprised because I have been sliding well and I felt like I was capable of doing this."
Latvia's Dukurs brothers grabbed the top-two spots on the podium for the second time this week. Martins was first at 2:15.54, while Tomass slid to the silver with a time of 2:16.63.
One of the most consistent sliders on the men's World Cup squad, Fairbairn had a breakthrough in the final race before Christmas in Lake Placid, N.Y., when he posted a career-best sixth. He backed that result up with another sixth place finish on Friday in St. Moritz, Switzerland.
"I think my consistency is paying off as the season continues," said Fairbairn. "My results earlier this year have given me a lot of confidence for each race, and I'm going to ride that all the way to the Olympics."
Fairbairn became just the fifth Canadian male to win a World Cup medal since skeleton made its Olympic debut in 2002. He is also the first male to strike the World Cup podium since Jon Montgomery won gold in Whistler in the post-Olympic year.
"It was pretty cool and means a lot to snap the drought and to be in the company with other Canadian sliders that have a World Cup medal," said Fairbairn, who sports a human brain painted on his race helmet. "It adds to my confidence heading to Sochi. I know that if I continue to follow the process, and can be at my best that I can be right there every week."
Eric Neilson, of Kelowna, B.C., was 10th (2:17.75), while Jon Montgomery, of Eckville, Alta., placed 18th (2:18.88).