Stony Brook entered the game undefeated (5-0) and ranked seventh nationally.
Florida's defense forced 15 turnovers and only allowed 23 shot attempts.
Freshman midfielder Brianna Harris chipped in with a career-high five draw controls.
Junior attacker Shayna Pirreca had a perfect four-for-four shooting day, and added an assist.
Senior attacker Mollie Stevens filled the box score with seven goals, 10 draw controls, and four ground balls.