The Reds entered the round-four clash in third spot, one above the Rebels, but they looked a cut above for much of Friday night's match at AAMI Park.
Reds coach Les Kiss was delighted with the performance to clinch their first away win of the year.
"Some things to work on for sure, but to win on the road with 53 points, that's not bad," an understated Kiss said.
"There are some things we still have to work on, and we just put ourselves under a bit of pressure and gave them a chance to get back into the game there for a while.
"But I never thought we were going to yield that game."
The only downside to the victory was a knee injury to centre Isaac Henry, which Kiss said "didn't look good".
Queensland set up the win with five first-half tries to build to a 33-7 lead at halftime, then added three more after the break.
Lock Seru Uru was a stand-out, claiming two first-half tries as the Reds ran the Rebels ragged at the breakdown.
It was a particularly gutsy effort for the Queenslanders, who had a short turn-around after their rousing victory over competition heavyweights the Chiefs last round.
The Rebels were disappointing in the first half, with their highly rated forward pack, led by ex-Red Taniela Tupou, failing to match the pace of their opponents, with coach Kevin Foote making early changes.
Queensland's Tate McDermott catches a high ball. (Rob Prezioso/AAP PHOTOS)
Melbourne started the second half in better shape and were first on the scoreboard as they started to move the ball and reduce their errors.
They scored two tries, through winger Glen Vaihu and reserve prop Isaac Aedo Kailea, in the space of five minutes to close the gap to 33-19.
But their comeback was snuffed out when Vaihu gifted the Reds a try.
Stopping the ball going over the sideline, he threw it back inside - straight into the hands of Queensland centre Josh Flook, who strolled to the tryline.
The Rebels added another try through Tuaina Taii Tualima, but momentum was all the Reds' way.
They pushed past the half-century through reserve hooker Josh Nasser and Flook, who added a second to wrap up a comprehensive win.
Melbourne skipper Rob Leota said his team failed to execute their game plan and paid the price.
"We were passive on defence and the coaches did a really good job to set us up well and we just weren't there in the first half, and we've got to be better against a good team like the Reds," he said.
"That's on us, to be able to deliver on the game plan."
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