UCSC (3-6) broke a six-game losing streak while sending Mills (0-8) to their eight straight loss.
Shaw got UCSC on the board in the 20th minute off a pass from Tomiko Hoshjima. The rest of the half was played at an even pace however with only six shots combined between the two squads in the first 45 minutes.
UCSC turned on the switch in the second half, outshooting the hosts 11-0. The Cyclones were able to hold off the Slug attack until the 75th minute, when Colasin clinched the game with her goal.
UCSC had two more shots in the last three minutes to add to their lead, but a last-second shot off a corner went high.
Overall, the Banana Slugs had a 15-2 shot advantage. Malia Starita had a stop in the first half on Mills' only attempt on frame.
Anais Uriarte had five saves for Mills.
The Banana Slugs next have a pair of home games against Division II opponents, starting on Thursday against Cal State Monterey Bay.