Successive defeats by the Stormers and Bulls effectively ended the New Zealand team's chances of reaching the finals stage but they were much improved against the Cheetahs, outscoring them four tries to three.
"There were some questions asked of us before the game but now we have the win it feels a whole lot better. We knew we had to be more physical and the boys answered the call," Hurricanes skipper Victor Vito said in a TV interview.
Flyhalf Beauden Barrett scored 24 points for the New Zealanders, including their opening try, while Vito, Julian Savea and TJ Perenara also dived over.
Prop Coenie Oosthuizen grabbed two tries for the Cheetahs and centre Robert Ebersohn added another.
The teams were level 12-12 at halftime before the Wellington-based side upped the pace of the game in the second period.
"It was not a good game for us especially in the second half," said Cheetahs captain Adriaan Strauss. "They kicked in behind us a lot and we just shifted the ball from side to side.
"We didn't want to play from our own 22 but we did that and it was very costly. We need to make a big step up next week, everything that went wrong tonight we can fix against the Reds." (Reporting by Nick Said in Cape Town; editing by Tony Jimenez)