The result ties the AHL North Division best-of-seven semi-final series 2-2 and gives the home-ice advantage back to Rochester. Anthony Stewart led Rochester with two goals, including the winner.
The Bulldogs outshot Rochester 23-19, but had only two shots in the third period and never really threatened to tie it after the Americans took a 4-3 lead early in the third.
Carey Price, the 19-year-old rookie, has looked very average. Price gave up three goals in his first 11 shots on Saturday in Rochester, three in his first 12 shots Sunday at home and then three in his first 11 shots again Tuesday night.
The Bulldogs started the game like they wanted to end it early. They took the play to the Americans right from the opening faceoff and were up 2-0 before the period was 10 minutes old.
Cory Urquhart scored a goal-scorer's goal at 6:57 to give the Dogs a 1-0 lead. He pulled Rochester goalie Craig Anderson far enough to one side, then went back to his forehand and fired it in the open net.
Jonathan Ferland made it 2-0 for Hamilton at 9:54.
The Americans got back in the game at 15:14 on a goal by Stewart. Michael Ryan scored his fourth of the series, on a power play to tie it.
Marek Zagrapan gave the Amerks a 3-2 lead before the Bulldogs tied it on a goal by Ajay Baines.
Stewart scored the winner at 4:22 of the third.
The series resumes Wednesday night in Rochester, N.Y., War Memorial with Game 6 back at Hamilton's Copps Coliseum on Saturday.
If a seventh game is necessary it would be played in Rochester on Monday.