Matt Climie was incredible again as he held the Stars in it while getting outshot 28-5 in the first half of the game.
Texas trailed 2-0 at the time, but came back and won 4-2.
Climie, who had 51 saves in Game 6, had 41 in this one as Texas was outshot 43-20 and had no power plays. Hamilton was 0-for-3 on the power play.
Stars move on to face Hershey in Calder Cup Final for AHL championship.