Cheney (#38 Chevrolet Camaro) capitalised on a fierce contest between Nash Morris (#67 Ford Mustang) and Ben Gomersall (#32 Mustang) to take an unchallenged victory.
Morris and Gomersall rounded out the top three, ahead of Joel Heinrich (#16 Mustang) and Brock Paine (#33 Camaro).
Gomersall led the field away after qualifying on pole on Saturday morning, while Hayden Hume missed the start, being pitched sideways after contact from Alice Buckley.
Cheney pushed for the lead at Turn 2, being forced wide on the exit of the switchback through Turn 3, allowing Morris through to second.
Drama erupted behind the leaders with Robbie Farr, Ben Kavich, Cameron Laws and Clint Rayner all caught up in an incident.
The safety car was deployed as Farr was left stranded at Turn 4 with heavy rear bodywork damage, returning to the pits for the remainder of the race alongside Rayner.
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As the yellow flag waved, Kody Garland and Des Collier each spun at the final corner in separate incidents.
When the green flag waved, Gomersall continued to lead following the restart, with Morris latched onto the rear bumper.
Morris dived for the lead at Turn 2, attempting to shut the door on Gomersall at Turn 3, but being forced wide and allowing Cheney back into the fight.
Gomersall and Morris continued to exchange blows for two laps, eventually coming together at the final corner and allowing Cheney to easily take the lead at the end of the pit straight.
Hume (#45 Mustang) recovered from the start issue to finish sixth, ahead of Jackson Rice (#37 Camaro) and Buckley (#150 Camaro).
Tommy Smith (#116 Camaro) struggled for outright pace to finish ninth ahead of Aussie Racing Cars regular Scott Dornan (#23 Mustang) in his TA2 debut.
The TA2 Muscle Car Series returns for its fourth and final race of the weekend at 8:30pm AEST.
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