Italy's Arianna Fontana, who won gold in the 500 metres, took bronze in the final during which two South Korean favourites, Shim Sukhee and Choi Minjeong, crashed.
"I really can't believe it. It's incredible that it just happened today," Schulting told reporters. "I was just enjoying the final at first and I think that's why I won the gold, because I was enjoying it so much."
The Koreans' crash occurred on the final lap when they rounded the penultimate turn, bumped into each other and slid into the sidewall. Shim was handed a penalty for impeding.
"At the end we got tangled, and I think then we fell down," Shim said.
"I feel sorry for that and at that moment I was worried if Minjeong got hurt. She said she’s OK, but I still feel sorry for her."
Schulting, who finished seventh in the 1,500 metres, led from about the midway point after jockeying back and forth with Boutin in the early laps.
For Boutin, the silver medal was a welcome step up from her bronzes in the 500 and 1,500 metres.
"I don't know how to express that but it's just, I'm proud of myself, all the work I did with all my team mates and all my staff is just incredible," Boutin said. "I know that I couldn't do that alone."
Fontana held on for third.
"It feels great. I didn’t think it could be possible, you know the 1,000 metres is not my best race, but today I started good and I felt good," the Italian said.
(Reporting By Dan Burns; Editing by Amlan Chakraborty)
