The Canadian was .41 seconds behind Shiffrin.
Gagnon captured bronze in a World Cup super-G last month in Garmisch-Partenkirchen, Germany.
"Today went well. Overall, I'm happy with the solid result," Gagnon said. "I was pushing to get on to the podium, but I lost a bit of time in the middle."
Gut-Behrami mastered the sun-bathed Olympia delle Tofane course to finally win the only medal missing from her storied career.
The 2016 overall World Cup champion beat Swiss teammate Corinne Suter by 0.34 seconds, living up to her billing as the main favourite after winning the last four super-Gs on the World Cup circuit.