Swedish veteran Frida Hansdotter took gold and Shiffrin failed to make the podium but the 24-year-old Holdener was delighted to become the first Swiss since Vreni Schneider in 1994 to medal in women's slalom.
Her success was built on an excellent opening run where she was first out and fastest but she was unable to drive home the advantage, missing out on gold by 0.05 seconds.
"I never could show two runs of good skiing together in my career in slalom but it's not so bad to get second," she told reporters.
"The time will come I hope where I can show two good runs and stand up top but if you had asked me this morning about a silver medal I would have signed for it there and then," she added.
Holdener, who has never won a World Cup slalom race, is hoping to add to her medal count.
"This gives me confidence for the next races – I’ve got the combined and the team event and the pressure will not be as high as today," she said.
"It was a good experience because I hope in the future to have more occasions where I am standing there as leader from the first run."
The bronze medal was a major surprise with 20-year-old Austrian Katharina Gallhuber, ranked 10th in the World Cup slalom standings, finishing above strong favourite Shiffrin,
"I can't believe it. I am speechless. I did not expect it. I have not been on the podium before. It feels like a dream, I hope it's real. I have no words for this moment" Gallhuber said
"My second run was really good. I stood on the start and thought 'All in' because I was really far behind."
(Reporting by Simon Evans, editing by Ed Osmond)
