The Reds led 21-5 in Friday night's Super Rugby Pacific match at Suncorp Stadium before the Drua snatched back the lead early in the second half courtesy of a Manasa Mataele hat-trick.
But Queensland's set-piece dominance at the scrum and line-out turned the match, with a four-try burst following Mataele's magic lifting the Reds to victory.
The bonus-point win improved Queensland's regular-season record to 8-6.
But their hopes of landing fourth spot were already extinguished before Friday's match after the Crusaders crushed the ladder-leading Hurricanes 47-14 earlier in the night.
It means the Reds (37 points) are likely to finish sixth, assuming the Brumbies (33 points) beat the last-placed Moana Pasifika in Canberra on Saturday.
Queensland's win against Drua (5-9) came at a major cost, with Paisami limping off in the 28th minute after hurting his heavily-strapped left knee when tackled to the ground.
The 28-year-old cut a despondent figure on the bench in the second half while sporting a big knee brace, with scans to determine the extent of the damage.
"I haven't got the full story at this stage," Reds coach Les Kiss told Stan when asked about Paisami's injury.
"Obviously concerned if he isn't going to be all right. Hopefully Hunter's OK."
Mataele scored the opening try in the 12th minute when he intercepted a pass from Reds playmaker Carter Gordon before sprinting 60m to the line.
Queensland hooker Matt Faessler hit back for the home side in the 25th minute following a successful rolling maul.
A sharp pass from Josh Flook while he was falling to the ground set up Filipo Daugunu for a 30th-minute try.
And the score ballooned to 21-5 when Daugunu turned provider for Flook to score in the 34th minute.
The Drua hit back on the stroke of halftime, and it was the Mataele show early in the second half as the former Force flyer added two tries in the space of four magical minutes.
Mataele collected his own dribble to score his second try of the night.
And the hat-trick was complete in the 48th minute when Virimi Vakatawa's kick bounced upright, allowing Mataele to jump high to collect before racing to the line.
"It's pretty special, but I would trade that for a win any time," Mataele said after the match when asked about his hat-trick.
Queensland hit back hard via the set piece.
Harry Wilson scored in the 55th minute from a dominant scrum, and yet another powerful rolling maul from a line-out led to Faessler's second in the 59th minute.
The floodgates were officially open by that stage, with Seru Uru and Richie Asiata also getting in on the fun to secure victory and a bonus point.
Star Reds fullback Jock Campbell revealed at halftime he was dealing with a little groin niggle, but backed himself to be fit for the first week of finals.
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