The River Rats (2-1-0-0) opened the scoring on the power play at 5:46 of the first period when Scott Kelman scored his first goal of the season. Kelman, parked in front of the Bulldogs (1-2-0-0) net, tipped home a shot by Pat Dwyer.
Albany increased their lead to 2-0 at 17:04 of the first period when Aucoin took a long lead pass from Shane Willis and beat goaltender Yann Danis with a high shot to the glove side.
The Bulldogs cut the River Rats' lead in half when rookie Matt D'Agostini scored his first career AHL goal with Hamilton shorthanded.
Aucoin soon restored Albany's two-goal lead with the eventual game-winner at 13:18 of the third period.
Duncan Milroy rounded out the scoring with Hamilton's second short-handed goal of the game at 16:27 of the third period.
Albany goalie Justin Peters made 24 saves.
Bulldogs goaltender Yann Danis stopped a third-period penalty shot by forward Matt Murley, as well 17 of the 20 shots he faced overall.