Woods made two free throws to put Troy ahead 64-58 with 25 seconds left.
Zay Williams had 15 points and nine rebounds for Troy (1-0). Nick Stampley added nine rebounds.
Travion McCray had 14 points for the Catamounts (1-1). Mason Faulkner added 13 points and nine rebounds and Matt Halvorsen had 11 points.
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