Brown beat Hurricanes goaltender Corbin Boes 3:40 into OT to complete the comeback after the Warriors scored three unanswered goals in the third period to tie the game.
Brayden Point and Alexander Chirva also scored for Moose Jaw (6-7-3), while Zachary Sawchenko finished with 23 saves.
Griffin Foulk, Tyler Wong and Axel Blomqvist had singles for Lethbridge (2-11-2), and Boes stopped 35 shots.
LETHBRIDGE, Alta. -- Travis Brown scored twice, including once in overtime, as the Moose Jaw Warriors rallied past the Lethbridge Hurricanes 4-3 in the lone Western Hockey League game Thursday.