Brouwer has four tallies over his last two games for the IceHogs, who won for the first time in eight trips to Chicago this season and now hold a 3-2 series lead heading into Game 6 at the MetroCentre on Sunday.
After a scoreless first period, Rockford netted three goals before the second period was 10 minuets old. Jack Skille and Colin Fraser each scored unassisted at 2:08 and 5:45, respectively, and Brouwer potted a shorthanded marker at 9:11.
AHL MVP Jason Krog pulled the Wolves within 3-1 at the 18:27 mark, scoring his first goal of the playoffs after posting 12 assists.
Rockford goaltender Corey Crawford stopped 40 of 41 shots in the winning effort.
The IceHogs can advance to the Western Conference finals with a home-ice win over Chicago in Game 6 on Sunday.
With the victory, the division-champion Marlies staved off elimination and forced a Game 6 on Saturday back at the Onondaga County War Memorial in Syracuse.
Crunch defenseman Clay Wilson pulled his club even at 3-3 with a power play goal 2:17 into the third period. The game remained deadlocked until Battaglia’s game-winner.