In Melbourne, hard-running centre Lachlan Mitchell scored after the halftime siren to hand the Rebels a 13-10 lead at the break but the Reds steamed back to secure their third successive victory and their fifth straight against the Rebels.
Melbourne's only win of the season was in round one against the Force when they trailed at halftime; they also lost when the Brumbies and NSW came from behind.
The Rebels' chance of a late fightback suffered a setback when a penalty kick, about to be taken by Wallabies star James O'Connor, was reversed by Argentine referee Francisco Pastrana on the advice of Television Match Official George Ayoub, who nabbed hooker Ged Robinson for over-vigorous rucking.
The Reds looked to have scored immediately down the other end through fullback Jono Lance, however he somehow failed to get the ball down.
Three missed penalty kicks by stand-in skipper O'Connor also proved crucial and put a dampener on his 50th Super Rugby appearance.
The Reds were quick to put the knife into the Rebels' second-half hopes with halfback Nick Frisby, in his first start in the No.9 jersey, scoring after some good lead-up work by centre Anthony Faingaa, in his first game this season after a hand injury.
Quade Cooper converted from the sideline and then a penalty kick at the 60-minute mark pushed the lead out to 20-10.
With a couple of breaks out wide and some fierce tackling, Rebels No.8 Scott Higginbotham did his best to rally the team in his first outing against his former side.
But the Rebels lost momentum following the Lance no-try.
But they delivered an impressive first half, with Mitchell's try well deserved.
Electing for another scrum five metres from the tryline rather than a penalty shot, the Rebels attacked the line before halfback Nick Phipps found the hard-working O'Connor.
He held the ball up long enough for Mitchell to run the perfect line, scooting between defenders to touch down.
Queensland's first-half try was scored by centre Ben Tapaui.
A penalty kick by Cooper with just over a minute remaining compounded the misery for the Rebels, who missed out on a bonus point for finishing within seven points.
Meanwhile in Friday's earlier Super Rugby match at Wellington's Westpac Stadium, the Hurricanes prevailed in a thriller over the Crusaders 29-28.
A sharp-looking Dan Carter and an up-tempo second half looked to have secured the win for the Crusaders as they ran in three second-half tries to lead 28-19 with less than 20 minutes remaining.
Down by six and with eight minutes remaining, the Hurricanes roared back as winger Alapati Leiua latched onto a loose Adam Whitelock pass, with the Crusaders hot on attack, and ran away for the match-winning try.
The first half was peppered with too many handling errors and turnovers early on, both sides unable to build phases or establish any sort of consistent pressure.
And while the Hurricanes opened their scoring early through a Beauden Barrett penalty in the seventh minute, it was the Crusaders who scored the only try of the spell.
Inside centre Ryan Crotty created something from nothing on 25 minutes after the Crusaders forced a turnover 35 metres out, weaving through some indifferent Hurricanes tackling to score the southerners' first try of the season.
The Hurricanes' defensive line found it difficult to regather, but the Crusaders' poor handling left them unable to capitalise on the missed tackles and three Barrett penalties in the last six minutes before halftime gave the home team a 12-7 lead at the break.
The Crusaders bounced back with two early second-half tries to take the lead 21-12 after 52 minutes. Hooker Corey Flynn crashed over six minutes after the restart, then fullback Israel Dagg showed great pace and control to toe ahead a turnover and touchdown.
Giant Hurricanes winger Julian Savea monstered Tom Marshall and then Dagg on his way to the line four minutes later to reduce the deficit to two.
However, Carter replied just after the 60-minute mark, kicking ahead and waiting for the bounce to touch down before adding the conversion for a 28-19 lead.
Barrett's 70th-minute penalty - his fifth of the match - gave the Hurricanes a glimmer of hope, and Leiua's intercept try wrapped up an unlikely win.