Halfback Nick Frisby crossed twice while Curtis Browning scored his first ever Super Rugby try, but the Reds had to hold on grimly in the dying minutes - and with a numerical disadvantage, following flanker Liam Gill's 69th-minute yellow card - as the fast-finishing Cheetahs applied the pressure.
The Reds were diabolical in the first half, making seven handling errors as the visitors opened up a 10-3 lead through Uzair Cassiem's try in the 34th minute.
That also came with the Reds a man down, with Anthony Fainga'a needlessly earning himself a spell in the sin bin for a late off-the-ball hit on his opposite number Michael van der Spuy.
But Queensland's scrum was dominant as usual and they eventually recovered from their shocking start, with Browning peeling off the back of a scrum to touch down after the half-time siren and Frisby's two efforts, in the 46th and 63rd minutes, both finishing off neat team moves.
Reds captain James Slipper said the sapping humidity was the reason why the game was so disjointed.
"Everyone was pretty sweaty, the ball was really slippery and both teams fell into that scrappy, grind game," he said.
"We couldn't really execute anything and that's probably fair for both teams ... we wanted to play with the ball, but we're pretty happy with how the game turned out.
"I think our bench came on and did a really good job."
The Cheetahs were denied a last-minute try to winger Raymond Rhule, which was chalked off due to a foul play incident involving reserve Willie Britz, who appeared to punch Rob Simmons in a scuffle away from the ball.
Britz was yellow-carded but coach Franco Smith complained the footage was inconclusive.
"You can't see on the video if his hand made contact. He might have just touched the ground with an aggressive action," Smith said.
"I felt it was inconclusive but I'm not going to criticise what's happened, we should have been in the game before that."
- AAP
