Roxbury nearly tied it with about seven minutes left, but Allison McGuire made back-to-back saves to keep it 1-0.
McGuire finished with seven saves. Lisa Boyke stopped nine shots for the Rockets.
Gilboa (1-1) will open league play today against visiting South Kortright.
On Saturday, Gilboa will play Jefferson in a tournament consolation game at 10 a.m.
Downsville 3, LM 1
Kaileen Townsend scored two goals to lead the host Eagles to the title in the Flannery Tournament on Saturday.
Townsend scored her first goal from 25 yards out, finding the left corner with 13 minutes remaining in the first half. Less than two minutes later, she scored again for her fifth goal of the tournament.
Leigha LaTourette scored off a header with nine minutes to play for Downsville (2-0), which hosts Hunter-Tannersville on Tuesday.
Sullivan West 2, Walton 1
Katie Maguire scored on a penalty kick with 15 minutes seconds left in the first half to tie the score at 1 for Walton, but Sullivan West scored the winner 26 seconds into second half to win the consolation game of the Flannery Tournament at Downsville.
Walton (0-3) will travel to Unatego on Wednesday.
Sidney failed to score in the Greene Tournament, following a 3-0 first-round loss to Susquehanna Valley with a 2-0 setback against Windsor in the consolation game.
Backup goalie Carlee Bargher made 10 saves against SV, which took a 2-0 lead into halftime.
Bargher also made six saves against Windsor but gave up two breakaway goals to Sheree Baker in the second half.
“Carlee has done a great job in Jo’s absence, especially since she has had no formal training (as a goalie),” Sidney coach Jody Gravelin said, referring to injured goalie Jolene Krom (mild concussion). “Carlee is an athlete and has good instincts. She made a few great saves over the weekend.”
The Warriors host Delhi on Wednesday.