The skier from Sudbury, Ont., finished the men's 15-kilometre race 25.2 seconds back of Switzerland's Dario Cologna, who won with a time of 40 minutes 12.4 seconds.
Lukas Bauer of the Czech Republic was second, finishing 24.0 seconds back.
"I went out really hard today. I went for the win and I don't regret it," said Kershaw, who won his first World Cup medal of the season. "It has been a hard couple of weeks for me personally and I didn't know what to expect coming off the Tour. Today I was able to mentally switch off the brain and focus on skiing, which felt amazing."
In the women's 10-kilometre race, Poland's Justyna Kowalczyk won the with a time of 29:44.8 to beat Marit Bjoergen of Norway by 21.9 seconds. Therese Johaug of Norway was third, 40.5 seconds behind.
Cologna and Kowalczyk also both won the sprint races a day earlier.
Cologna took the men's 1.4-kilometre sprint, while Kowalczyk won the women's 1.2-kilometre sprint.