The 35-year-old Guay's compatriot Manuel Osborne-Paradis caused another shock by finishing third after many of the top contenders struggled to master the 2km course.
All three men on the podium were in their 30s with Guay becoming the oldest world champion in Alpine skiing and only the fourth man to win world gold in both Super-G and downhill.
"It's incredible. I'm as happy as can be," said Guay who has battled back from knee surgery in 2015.
Jansrud, who is also the discipline's World Cup leader, must have thought he had done enough after a near-flawless run saw him leapfrog Austrian upstart Vincent Kriechmayr who set the early pace but eventually finished fifth.
The red-hot favourite was able to breathe a sigh of relief after seeing Norwegian Aleksander Aamodt Kilde cross the finish line 0.09 seconds behind him before Guay, the 2010 World Cup Super G winner and the 2011 downhill world champion, toppled the two Norwegians.
Gliding down the course he gained precious time on the treacherous jumps and stormed to the finish as the crowd roared.
"I am happy to be here as the race leader after a big crash I had in Garmisch-Partenkirchen (downhill World Cup race) last month," Guay told Eurosport.
Osborne-Paradis, who had never before enjoyed a podium finish at the world championships, celebrated his 33rd birthday by beating Kilde to the bronze medal after starting 26th.
Guay looked delighted as his team mate crossed the line.
"It's always nice to share your success with a team mate and I almost feel as if it's my birthday," he said.
Jansrud put on a brave face. "I skied to the best of my ability and I am very happy to be on the podium."
(This version of the story ammends slug, no change to text.)
(Writing by Zoran Milosavljevic; Editing by Martyn Herman)
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