Jansrud's victory was his first at the Alberta ski resort west of Calgary. Osborne-Paradis of North Vancouver, B.C., tied for second with Guillermo Fayed of France for the Canadian's first World Cup medal since 2010.
"It feels really good," Osborne-Paradis said. "I was nervous today because I knew I could be on the podium. This was the best chance I've had in a long time."
Jansrud conquered the 3,133-metre course in one minute 50.20 seconds. Osborne-Paradis of North Vancouver, B.C., and Fayed posted identical times of 1:50.34.
Jansrud won gold in super-G and bronze in downhill at the Winter Olympics in Sochi, Russia, in February.
His countryman Aksel Lund Svindal has dominated at Lake Louise with three straight super-G wins plus a downhill victory two years ago. But Svindal tore his Achilles' tendon playing soccer last month and could be out for the season.
Jansrud, 29, ensured the Norwegian anthem played again at Lake Louise.
"Lake Louise is not one of our toughest hills, but it's real tough to ski fast," the Norwegian said. "It's not really forgiving to ski on. If you stay on your edge for half-a-metre too long and then you're gone. It was tough skiing. It's not easy.
"It's like skiing on a wooden floor. Smooth, but that also makes it hard to be fast because you know it's going to be the same for everybody. It's tough, but for me, it worked out nice."
The men race a super-G on Sunday before heading to the World Cup's next stop in Beaver Creek, Colo.
"I will not be celebrating because we have the super-G tomorrow," Osborne-Paradis said. "Bummer."
Saturday's race was held in clear, cold conditions with a temperature of minus-24.
Jansrud and Osborne-Paradis were first and second respectively in Wednesday's training run. The next two training sessions were cancelled because 50 centimetres of snow fell on the mountain parks in 48 hours.
"I think it probably helped with having only one training run," Osborne-Paradis said. "Guys were dealing with, probably dealing with, confidence issues. I can't totally speak for them.
"For myself, when I don't have a great training run, it is a different mental state you have to be in to push it (in the race) when you only have one."
Fayed turned 29 on Friday and his belated birthday present was the first World Cup medal of his career.
"I was very surprised when I saw my time," the Frenchman said. "I did a very good run, but you never know if you are fast or not.
"Because we had just one training, I was very good physically. Not tired."
Lake Louise is the lone Canadian stop on the World Cup alpine ski circuit. Osborne-Paradis's silver medal Saturday was Canada's first there since he won super-G in 2009.
Osborne-Paradis was also second in the Lake Louise downhill in 2006 for his first career World Cup medal. But he didn't race for almost two years after he broke his leg and tore a ligament on Jan. 29, 2011.
"One race, first race of the season, I'm going to try and get on the podium at every race so it just helps," the 30-year-old said. "So far we're one-for-one."
Osborne-Paradis lives in Invermere, B.C., which is 146 kilometres southwest of Lake Louise. He married Lana McIntosh on Sept. 20.
From the prize purse of CDN$118,000 for Saturday's race, Jansrud earned $35,000 for the win. Osborne-Paradis and Fayed each picked up $23,000 as runners-up.
Calgary's Jan Hudec, an Olympic bronze medallist in super-G, was 19th. Ben Thomsen of Invermere finished 29th, Dustin Cook of Whistler, B.C., placed 36th, Jeffrey Frisch of Mont-Tremblant, Que., was 44th and Morgan Pridy of Whistler came in 54th.
Former world downhill champion Erik Guay of Mont-Tremblant did not race Saturday. Canada's most decorated World Cup ski racer with 22 medals has delayed the start of his racing season after a pair of off-season knee surgeries.
Hudec was frustrated with his result because he felt strong and fast on his skis. He won the downhill at Lake Louise in 2007.
"It's not a survival course, but it's a look-for-every-minute-detail kind of course," Hudec said.
"That's what makes it different from other courses which you can overcome with survival skiing and just attacking it, whereas this, you have to be like cat . . . a sneaky cat. And nobody likes sneaky cats, but that's what you've got to be to be fast here."