The game was decided in the third quarter where the Thunderbirds outscored the Hawks 5-1.
Cody Jamieson and Dawson Theede each scored three goals and dished out three assists and Warren Hill made 45 saves.
Halifax improves to 9-7 and Rochester falls to 6-8.
Up Next
Fri Apr 5 Halifax at Vancouver 10:00 PM ET
Sat Apr 6 New York at Rochester 7:00 PM ET