He led after Saturday's first heat, which was nullified by race officials because of "track conditions."
With Canadian team officials agitated at the finishing dock below, Edney put on the helmet designed especially for him and the race.
He laid down an even faster time in the second heat to win on his home track at Canada Olympic Park.
The helmet depicting a snarling bear and raking claws had been presented to him a day earlier by 19-year-old artist Richard Flamenco, who has a rare incurable skin disease that causes painful blisters on fragile skin.
Flamenco stood with Edney at the finish line. Together, they watched as the remaining sliders fell short of Edney's time of 46.146 seconds.
"There was a sense of calmness today with this helmet," Edney said. "It's hard to explain, but as soon as I put that helmet on, it felt like I had all this confidence and all this strength and I felt like I could put down two really good runs."
It was both Edney's first victory and World Cup medal of the Calgarian's career. The three-time Olympian's previous best result was fifth.
World Cup leader Felix Locht of Germany, who was fourth in the first cancelled run, finished second in 46.255. American Chris Mazdzer was third in 46.263.
Edney's victory gave the host country four medals in the Viessman Luge World Cup Calgary across the three disciplines of men's and women's singles and men's doubles.
Calgary's Alex Gough and Arianne Jones took silver and bronze in women's singles the previous evening. The doubles team of Tristan Walker of Cochrane, Alta., and Justin Snith of Calgary also earned bronze Friday.
The Federation Internationale de Luge (FIL) introduced new sprint races this season in men's and women's singles and doubles. The clock starts lower down the track and the fastest to the finish wins.
The world's governing body of the sport is testing the event, but is awarding World Cup points in it. The second sprint was held in Calgary with Gough winning the women's race Saturday. Edney was third in the men's sprint.
Gough made history in 2011 when she became the first Canadian to win gold at COP. Prior to that, the only Canadian medal there was Tyler Seitz's bronze in 2002.
So in addition to Edney making history in men's singles, it was the most successful World Cup ever for a Canadian luge team.
The performance lifted the cloud of Sochi hanging over the Canadians. They just missed winning the country's first Olympic medal in luge three times with fourth-place finishes.
"The Olympics was a tough thing for us," Edney acknowledged. "We knew we went in there the best we've ever been and I think we really wanted to prove to Canada that we are up there to compete with the best and we carried that through the summer.
"There were tough days out there, going to the gym and telling yourself you're wanting to continue to push to be the best. I think all that hard work we've put in over the years is finally paying off."
The plan was to auction the helmet off on www.Helmets4Heroes.com with the proceeds going to the Alberta Children's Hospital. Edney might have a hard time giving up his lucky head protection now.
"To see my helmet on Sam and going down this luge was a miracle," Flamenco said. "I was just so happy to see my helmet on a big screen."
Canadian head coach Wolfgang Staudinger thought Edney's mental resiliency Saturday stemmed from Olympic experience.
"That comes back to the Olympic hangover," Staudinger said. "The way I look at it, we went through so much disappointment in Sochi by missing out by very little. I think this hardens you mentally.
"I think that's where this comes from, that he knows he has to do a job first before he starts celebrating and he did the job and he ended up where he ended up now. A great day."
Rain changed to snow during the men's first run. No country protested the results of the first heat but race director Steve Jepson of Canada and three technical delegates made the decision to nullify the first heat.
"We had to annul the first run due to weather conditions and track conditions," said FIL's sport director Marie-Louisa Rainer. "We were in the middle of the race and it began to snow. We had weather changing all over the place, one snow, one rain and it was definitely not fair to the sport, to the athletes."
Edney may have been calm about the alteration. Staudinger, Luge Canada executive director Tim Farstad and Seitz, now manager of the Calgary track, were stressed out after the cancelled first run.
Staudinger had only 10 minutes after the final racer to launch a protest, but he was at the top of the track working on sleds at that time. Edney's victory dispelled the building tension.
"Between the runs it was a lot of confusion and disbelief and not understanding why we came up with the decision of cancelling the first run," Staudinger said. "Now I'm happy."
Calgarians Mitchel Malyk was ninth and John Fennell 19th.
Canada was shut out of the medals in the first two World Cups this season, which Edney and Gough didn't race. Gough was focused on her engineering studies and Edney was managing a nagging sports hernia.
Both will travel with the luge team Dec. 26 to Europe for the next World Cup race in Koenigssee, Germany.
Canada's luge team once took a back seat to the more successful sliding sports of bobsleigh and skeleton, but has a evolved into an international contender in a sport dominated by Germany.
"I was part of the team in those dark days when we weren't travelling with a physio and had one coach and were sleeping in vans," Edney said.
"We made the right decisions over the years. We've put in the hard work and this team has got a really good thing going for it."