The Coyotes won their sixth straight to maintain a narrow lead at the top of the Pacific Division. Going into Thursday's action, the five teams in division were separated by a single point.
Lauri Korpikoski tied it on a tip-in and Hanzal's wrist shot produced the final goal of the game.
Ilya Bryzgalov made 10 of his 33 saves in the third period to protect the lead. He has been in goal for every game during the current Phoenix winning streak.
Ondrej Pavelec took the loss, stopping 28 shots. The Thrashers have lost two straight.