The native of Mont-Tremblant, Que., dominated both her runs against Valeriya Tsoy of Kazakhstan to capture a bronze medal in the women's parallel giant slalom.
The competition is being held on the same course that will be used at the Sochi Olympics a year from now.
Former world champion and Olympic bronze medallist Marion Kreiner of Austria edged Amelie Kober of Germany by four-hundredths of a second to claim her third career World Cup victory.
Andreas Prommegger led an Austrian 1-2 in the men's event.
Prommenger dominated both runs in the final over Ingemar Walder to score his third World Cup victory this season. Rok Flander of Slovenia was 0.35 seconds ahead of Switzerland's Kaspar Fluetsch in the small final for third.
Not only had Lavigne never been on the podium, she had never finished in the top 16 at a World Cup event.
"I knew it could happen," she said. "In all the last races I was so close."
It all came together Thursday. She eliminated 2010 Olympic champion Nicolien Sauerbreij of the Netherlands in the quarter-finals
"It's been a great day," she said. "I'm really happy with the riding. I'm happy with the results. It feels good. It feels really good."
Parallel slalom events are scheduled for Friday. Lavigne is hoping for another good ride on the course she hopes to be competing on a year from now.
"It's a great opportunity to be here in Sochi to get to know the course," she said. "Hopefully I can do even better tomorrow."
Prommegger leads the parallel giant slalom standings after three events by 610 points over Roland Fischnaller of Italy. Fellow Austrian Lukas Mathies sits third.
Kreiner overtook Tudegesheva at the top of the women's standings, only 190 points in front of the Russian. Caroline Calve of Aylmer, Que., who finished 14th on Thursday, is third.
The snowboarders struggled on an icy course at the Rosa Khutor Exreme Park in the mountain cluster of the Sochi Games after days of warm weather, which forced the organizers to cancel slopestyle events scheduled for Monday and Tuesday.
Lavigne said she found Thursday's course "really long."
"That makes the day long and difficult," said Lavigne. "But hopefully I'll be fully recovered tomorrow."
Taku Hiraoka of Japan and Kelly Clark of the United States won the halfpipe events later Thursday.
Hiraoka scored 90.25 points on his first run to record his first career world Cup win. World champion Iouri Podlatchikov of Switzerland was second with 84.50, 1.25 points ahead of Vancouver Olympics bronze medallist Lago Scott of the United States.
Derek Livingston of Aurora, Ont., was the top Canadian in 26th.
Clark, the Salt Lake City Games champion, scored 88.25 points to claim her second World Cup victory this season. She was followed by Holly Crawford of Australia with 78.00 points. France's Sophie Rodriguez was next with 73.00.
Mercedes Nicoll of North Vancouver, B.C., was the top Canadian in 15th spot.
Lago leads the halfpipe world Cup standings with 1,960 points after four events. He is followed by China's Zhang Yiwel, who trails by 420 points. Luke Mitrani of the United States is third with 1,500.
Clark dominates the women's standings with 3,200 points. China's Liu Jiayu is second with 1,860. American Kaitlyn Farrington is another 20 points back in third.
"I was just happy to come here and get some experience in this pipe and at this venue," Clark said. "I'm happy with how I rode and looking forward to building my riding up."
— With files from The Associated Press