The 29-year-old raced the 2.7-kilometre Rosa Khutor course in the Russian Federation in one minute, 42.70 seconds.
Liechtenstein's Tina Weirather was second, 0.11 seconds behind, with Austria's Anna Fenninger in third, at 0.23 seconds.
For Suter, Friday's result was doubly important as it also acted as an internal qualifying race for the Swiss team.
"It's a difficult course. You have to be very present," Suter said.
"You have to be good on the ski, attack and control as well as you can," she said after the training run, which she was also the first to start.
"It's good to win today, but more important for me was to make the qualification for the Swiss team."
Fenninger, 2011 super combined world champion, top in Thursday's training, had been in the lead through every split time but took a wrong turn at a low gate that was being reset, which caused her to lose precious time.
Germany's Maria Hoefl-Riesch, the current leader in downhill and overall World Cup rankings, was 11th.
The women kick off their ski races on Monday in the super-combined, consisting of a downhill run in the morning, followed by a slalom in the afternoon.