Pita Sowakula, Atu Moli and Etene Nanai-Seturo scored first half tries for the Chiefs, who spent virtually all of the second spell defending as the Reds controlled the ball but were unable to breach the home side's impressive defensive line.
Taniela Tupou scored the only points of the second half with a try from a sustained buildup as the visitors hammered at the Chiefs' line.
The visitors forced the Chiefs to make 240 tackles in the game.
The Reds made less than 90.
Referee Angus Gardner initially awarded two tries to the Reds and one to the Chiefs in the first half but television match official Glenn Newman overruled all three.
The match was the last of the season in Hamilton for the Chiefs.