The Americans finished the American Hockey League regular season with a 48-30-1-1 record and 98 points. Hamilton ended at 43-28-3-6 and 95 points. The teams meet in the best-of-seven first-round series starting Thursday in Rochester.
Maxim Lapierre put the Bulldogs ahead with a short-handed goal at 9:13 of the first period.
The Americans didn't tie the score until Clarke MacArthur scored on a power play at 8:02 of the second.
Rochester goalie Craig Anderson made 25 saves. Rookie Carey Price stopped 29 shots for the Bulldogs.