The Heat, who once trailed 3-1 in this North Division semifinal, have rallied to force Game 7 on Tuesday night.
Rheault, who totaled six regular-season goals (6-5-11) in 44 regular-season AHL goals for Abbotsford, Manchester, and Providence, has now racked up five goals and six points in six postseason outings this spring.
Abbotsford took control of this one early, striking for three goals in a 2:09 span midway through the first period. Jason Jaffray began the Heat’s offensive attack 9:09 into the game, and Rheault made it 2-0 just 41 seconds later.
Rheault completed his hat trick midway through the third frame, with Sutter chipping his third helper of the afternoon.
Heat goaltender David Shantz turned aside 22 of 23 shots to pick up the victory. Amerks starter Tyler Plante was pulled after surrendering three goals on seven shots, and rookie Alexander Salak stopped 32 of 34 shots the rest of the way.