Saarinen, with a time of one hour, 31 minutes and 38 seconds, finished around a minute slower than Kowalczyk and Bjoergen.
Saarinen got off to a good start and kept her place with the fastest skiers throughout the race. After 25 kilometres, she stopped to change her skis and lost her third place for a while to Norwegian Kristin Steira, who shot by with a 15-second lead.
But the ski switch gave Saarinen a boost, and she powered through the last five kilometres to secure her place on the podium.
From the start of the race, it was clear that Saarinen was the only Finn contending for a medal. Her colleagues fell behind the top ten competitors pretty quickly.
Riikka Sarasoja finished 13th and Virpi Kuitunen 14th, while Krista Lähteenmäki was 26th.