Ben Tapuai and Nick Frisby touched down for the visitors, who scored 13 unanswered second half points in Melbourne despite periods of sustained pressure from the home side.
The Rebels have now led at half-time in three straight matches and lost them all. Their only victory this year came against the Western Force in round one, when they trailed by a point at the interval.
Quade Cooper kicked the Reds' other points but was outshone in his head-to-head duel with James O'Connor, his apparent rival to fill the Wallabies' flyhalf jersey against the British and Irish Lions later this year.
O'Connor set up the Rebels' only try for Lachie Mitchell, kicked the conversion and scored two penalties, although his evening was tarnished by three missed kicks at goal.
The Rebels put together 12 phases of possession at one point and camped deep into Queensland territory but could not find a finishing touch despite a stellar performance from number eight Scott Higginbotham.
Tapuai showed them how it should be done in the 15th minute, shimmying past his man and touching down for his third try of the season. Cooper, who had already hit a penalty, converted to make it 10-3 and the Reds could have been even further ahead but Anthony Faingaa spilled the ball as he twisted and rolled his way across the line.
"We still haven't put in an 80-minute performance this year," Reds prop James Slipper said. "We just played in patches which was not what we wanted to do."
The Rebels stayed in touch with two penalties from O'Connor but his accuracy wavered and Higginbotham's fleet-footed break amounted to nothing when a team-mate put a pass to ground with the line in sight.
The home side did lead at half-time thanks to O'Connor, who waited and waited to draw in several tacklers before popping up a soft pass for Mitchell to run onto and cross unopposed.
O'Connor converted but those two points were to be the Rebels' last.
Digby Ioane picked the ball up off his toes and broke the defensive line before offloading to Frisby, who accelerated away to score. Cooper converted for 17-13 after 43 minutes and then landed a penalty awarded for a late challenge by Luke Jones.
O'Connor thought he had the chance to trim the deficit after the referee awarded a penalty to the Rebels but the official reversed his decision when his TV assistant advised him that Paul Alo-Emile's swing at an opponent had been preceded by Ged Robinson's illegal use of the boot.
Play switched up the other end and Cooper's final penalty made sure of the result.
- Sports & Recreation