Carmel, which started its season Tuesday with a 17-10 loss to Brewster, trailed the Quakers 9-1 at halftime, before coming back to make the game closer in the second half.
Senior captain Emma Lowrey led Greeley with four goals and one assist, and senior co-captain Anna Waterhouse had a hat-trick. Ashley Heis had three goals and one assist for Carmel, and senior captain Caitlin Murphy went two and two.
Greeley coach Annamarie Marasco said the Rams are a team on the rise.
"Carmel really has improved from last year," she said. "We played them last year and it was a bit lopsided, but they have worked very hard, and you can see the improvement."
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