It was the Rangers who got out to a hot start, as they led 2-0 after 20, thanks to goals from Jaeger Lapointe and Darrin Chrisp.
In the second, the Thrashers cut the deficit to just one, but the Rangers came right back and restored their two-goal lead thanks to Carter Cockburn as he improved on his early success so far this season as the Rangers led 3-1 after 40.
In the third, the Rangers scored two goals, but the Thrashers doubled up that total and scored four in the final 20, as the game headed for extra time and eventually a shootout.
Jacy Kennedy ended up with the game-winner as the Thrashers beat the Rangers, 6-5.
The Rangers outshot the Thrashers, 35-32.
Both teams will return to the ice on Sunday afternoon at 2:00 for the quick two-game series finale at Credit Union Place.