Looking to atone for a crushing 48-6 loss at the hands of the Storm in round 17, the Broncos produced some of their best football of the season on Friday night to secure their fourth-straight win, moving level with the Cowboys and Bulldogs in fourth spot on the table.
Two first-half tries to centre Tom Opacic set the tone for Brisbane, who dominated possession in the opening term and withheld a determined Storm outfit after the break to ensure the race for the top four goes down to the wire.
The visitors clicked into gear from the outset, showing sublime ball-handling skills to stun the home side twice in early stages.
Sam Thaiday celebrated his 250th NRL game in style thanks to a stunning one-handed offload that caught the Storm defence off-guard to set up Opacic's opening try after three minutes.
Jordan Kahu's acrobatic effort in the right corner doubled his team's advantage five minutes later.
A rare foray deep into Brisbane territory resulted in Melbourne second-rower Tohu Harris reaching over from close range after 26 minutes to halve the early deficit.
But the visitors struck back with a Kahu penalty goal before cashing in on Marika Koroibete's dropped ball deep in Storm territory, allowing Opacic to score his second four-pointer with two minutes left in the half.
Melbourne looked more energetic after the break but could not wear down Brisbane's defence.
The Broncos made them pay with a polished back-line move that sent Darius Boyd over for a 20-4 lead after 55 minutes.
Ben Hampton appeared to breathe life into the Storm when he crossed for his first try of the season with 15 minutes left.
But fortune favoured Brisbane when a kick from broken play rolled into the Storm's in-goal area, with Cooper Cronk slipping in pursuit to allow Jai Arrow to wrap up the match.
The Storm could have secured the minor premiership with a victory, but now face the prospect of a winner-takes-all clash with Cronulla for the JJ Giltinan Shield in the final round, provided the Sharks beat the Roosters on Saturday night.
Brisbane coach Wayne Bennett was pleased to see his side take control of the match from the beginning.
"Our start was spot on - it had to be," said Bennett. They (Melbourne) always start well.
"You don't want to give them momentum and the boys were on from the kickoff.
"They kind of carried on from where they left off against Canterbury, so that was good."
Bennett also praised the pressure and attitude his players applied right across the ground.
Captain Corey Parker expressed pride in Brisbane's performance against the ladder-leading Storm.
"We had a game plan that we thought, if we could execute, we'd be right in it," said Parker.
"It's just really satisfying to be able to do that, particularly against a good side at (their) home.
"They stuck it to us and it was a good game of footy going on but 1-17 turned up and we got the job done."
While full of praise for the victors, Melbourne coach Craig Bellamy lamented another lethargic showing from his charges after similar recent first-half performances against South Sydney and Canberra.
"I just thought we were really poor defensively in the first half," said Bellamy.
"Especially at the start of the game, they scored two tries in the first seven or eight minutes.
"That put us behind the eight ball, to be quite honest," added Bellamy.
"We didn't really improve too much defensively in the first half.
"Our second half was a lot better but, by then, the horse had bolted."