It was the first win for new head Tim Soudan, in only his second game with the Rattlers.
Galloway, who was named as the Bud Light Player of the Game for his efforts, made 10 of his saves in the first half as the Rattlers held Denver to just three goals in the first half while building a one-point lead.
After the Outlaws took a 2-0 lead in the first three minutes of the opening quarter on goals from midfielder Nate Watkins and attackman Connor Martin, the Rattlers put together a three-goal run for a 3-2 advantage with 2:06 left in the period. Attackman Ned Crotty had a pair of assists during the run.
The teams traded goals in the second quarter before Rochester took a 5-3 lead on an unassisted goal by Crotty just 49 seconds into the second half. But, the Outlaws answered with back-to-back goals from attackmen Billy Bitter and Brendan Mundorf to tie the game at 5-5 with 5:08 left in the third quarter.
But, the Rattlers regained the advantage with back-to-back goals, including a two-point marker from midfielder Anthony Kelly, in a 25-second span for an 8-5 lead with 2:22 left in the period.
Trailing by a three-point margin, the Outlaws opened the fourth quarter with three straight goals to tie the game with 7:49 remaining in regulation. After midfielder Peet Poillon scored an unassisted goal, midfielder Steve Holmes followed by converting a Martin assist with 8:39 left. Less than a minute later, midfielder Bill McGlone tied the game with an unassisted marker past Galloway.
With 2:24 remaining in regulation, midifelder Jordan Levine gave Rochester a 9-8 lead when he scored his seventh goal of the season, an unassisted marker past goalkeeper Jesse Schwartzman.
While Galloway led the Rattlers' defense, Crotty scored two goals with two assists in the win for Rochester while Levine added a pair of goals.
Bitter, who was playing in his first game since June 18, scored two goals to lead the Outlaws while Martin added a goal with an assist. Schwartzman made 13 saves in a losing effort for Denver, which outshot Rochester by a 47-36 margin.
The Outlaws also had a 29-27 advantage in ground balls.