After finishing first and second in a Europa Cup event last weekend, the Australian Institute of Sport (AIS) scholarship holders upset many of the sport's established stars at the season opener in Igls, Austria.
Lincoln-Smith, 26, led after the first of two runs, but couldn't match the speed of Russian slider Olga Potylitsina on run two, and finished just 0.23 seconds behind to claim the silver medal.
Lincoln-Smth beat the first three placegetters in last season's Skeleton World Cup - German Anja Huber, Great Britain's Shelley Rudman, and Canadian Melissa Hollingsworth.
Lincoln-Smith was thrilled to finish on the podium for the first time in a Skeleton World Cup event.
"I was really pleased with the result. I knew I was capable of the win if I stuck to my game plan," Lincoln-Smith said.
"The team has been amazing this week and my coach, Eric Bernotas, is so good at calming me down and saying the right thing at the right time.
"I feel very lucky to have the team around me that I do."
Chaffer set the second quickest time overall on the second run, to move from 11th to sixth place, easily her best World Cup result.
"It was a pretty good day," Chaffer said. "My first run was going well until corner nine and then it slipped away from me.
"I was happy to be able to fix it in the second run and jump a few spots. It's a great way to start the season and I'm now ready for the next challenge."
Lincoln-Smith's silver medal equals the best result by an Australian in skeleton, which Michelle Steele achieved in Japan in 2007.
The Skeleton World Cup continues next weekend in La Plagne, France.