Jean-Francois Damphousse made 41 saves and Hamilton scored three times in the third period to defeat Cleveland, 4-3, in Game 4 on Thursday night.
The Bulldogs lead the North Division semifinal series three games to one, and can advance with a win back home on Friday.
Tomas Plekanec and Francois Beauchemin scored 22 seconds apart to turn a 2-1 deficit into a 3-2 Bulldogs lead, and after Cleveland pulled even again, Marcel Hossa netted the winning goal with 4:24 to go.
Plekanec, Beauchemin and Hossa finished with a goal and an assist apiece, and Ron Hainsey and Alexander Perezhogin recorded two assists each for Hamilton.
Shane Joseph, the Barons’ leading playoff scorer, had two assists for Cleveland.