Jimmy Lodge, Terry Trafford and Steven Strong scored in regulation for the Spirit (30-27-6), who snapped a four-game winless streak.
Saginaw was blanked on the power play in three chances while Kitchener went 2 for 8 with the man advantage.
Lodge opened the scoring 4:11 into the opening period, beating Gibson after sliding in his own rebound.
Corrado tied the game in the second period, deflecting Ben Fanelli’s shot over Paterson, but the Spirit grabbed the lead back when Trafford beat Gibson between the pads on a 2-on-1.
Strong made it 3-1 with a shorthanded goal at 16:27, but Murphy’s blast from the point 39 seconds later beat Paterson and cut the lead to one.
Puempel tied the game on the power play just past the midway point of the third period, snapping a shot from the high slot off the post and in.
Overtime solved nothing, sending the game to a shootout. Sutch and Kea scored for the Spirit, while only Puempel was able to get one by Paterson.