The win gives Hamilton (14-6) a 2-1 advantage over Hershey (13-4) in the best-of-seven series, with games four and five scheduled at Copps on Wednesday and Thursday.
Rookie goaltender Carey Price, 19, was sharp again for Hamilton, making 39 saves - 17 in the opening period alone - to improve his 2007 post-season record to 13-6.
Price made one of his best stops of the night on a Hershey man advantage early in the game. The rookie calmly flashed his glove to snag Tomas Fleischman's quick wrist shot from just outside the crease, preserving a one-goal lead.
The Williams Lake, B.C. native and the fifth overall draft pick of the parent Montreal Canadiens in the 2006 NHL Entry Draft leads all AHL playoff goalies in shutouts (two) and saves (593) and is now tied with Hershey's Frederic Cassivi for most wins.
Corey Locke and Matt D'Agostini added two assists each for Hamilton, while defenceman Dan Jancevski had a goal and an assist. Locke leads the Bulldogs with 22 points in the playoffs, passing former captain Jason Ward's record of 21 points in a single post-season (2001-02).
Groulx, 25, opened the scoring just 1:20 into the game with on a screened point shot on the power play and then added his second of the night, on another Hamilton man advantage late in the second period, capping a decisive 20 minutes of play.
Hamilton scored four times in the period to pull away from the defending champion Bears.
Benoit gave the Bulldogs a 2-1 lead early in the frame when he went hard to the net and deked Frederic Cassivi, sliding a back-hand shot into an empty net after just 1:19.
Ryan O'Byrne made it 3-1 Hamilton when he converted a pretty cross-ice feed from D'Agostini, redirecting the puck through Cassivi's five-hole at 7:58 of the second period.
Jancevski stretched the margin to three goals on his third of the playoffs. The big defenceman controlled a rebound in a goal-mouth scramble and tucked the puck behind Cassivi, before Groulx added his second.
Hamilton scored three power-play goals, while Hershey was just 1-for-11 with the man advantage, seven of those chances coming in the first period alone.
Jakub Klepsis had both goals for Hershey, while Fleischman assisted on each.
Klepsis scored his second of the game on a nice play, redirecting a pass from Fleischmann behind Price midway through the third period.
The Bears had four consecutive opportunities to reply on the man advantage after trailing 1-0, but couldn't get an equalizer.
After dominating the first period of play, Hershey finally scored with a power-play goal at 19:49 from Klepsis, who beat Price low on the short side after taking a feed from Fleischmann.
The Bears out-shot Hamilton 18-6 after 20 minutes.
Notes: Locke needed just 20 playoff games to notch the Hamilton record for most points in a single post-season, while Ward needed 23 games to tally 21 in 2001-02 ... Hershey went 1-for-7 on the power play in the first period ...Hershey right-winger Scott Barney was held pointless on the night. Barney leads the Bears with 10 playoff goals (10-9-19), two of which came in the 4-2 game two Hershey win at home ... The Bulldogs have not trailed in a series throughout their Calder Cup run.