In front of 50,188 fans, the Dolphins secured their greatest win in the "Battle of Brisbane" after trailing 24-0 on Saturday night.
Dolphins co-captain Isaiya Katoa laid on four tries to secure the club's 13th victory of the season and keep them in fifth position.
It was Brisbane's seventh consecutive loss at Suncorp Stadium for the first time in their history.
"We just need to be better around our defence," coach Michael Maguire  said.
"We all need to take ownership. Are we capable of being better than where we are? I believe so, definitely."
Tabuai-Fidow, who won the Battle Medal as man of the match, scored his second try in the 68th minute with stunning leap above Reece Walsh from a Katoa bomb to give the Dolphins a 36-32 lead, the first time they had hit the front.
"It's obviously a special round for myself, being a proud Torres Strait Islander. There's so many great Indigenous players out there as well," Tabuai-Fidow said.
"So to get the win in this round and especially against the Broncos, it's something special."
Cobbo's clinical finish in the corner, after Tabuai-Fidow's ripper, sealed the deal.
The Broncos led 30-24 after 40 minutes of electrifying rugby league, which featured nine tries.
Brisbane five-eighth Ezra Mam, also of Torres Strait Islander heritage, scored a first-half hat-trick to put his own indelible stamp on Indigenous Round.
Fellow Indigenous teammate Walsh was on fire and Dolphins duo Tabuai-Fidow and Cobbo conjured moments of pure magic.
Brisbane were scoring at better than a point a minute to lead 24-0 and stun the Dolphins.
The move by Broncos coach Michael Maguire to elevate Billy Walters, in his 100th match for the club, to No.9 worked a treat. Walters had an early 40/20 and line break to set up centre Deine Mariner for a try.
Mam was unstoppable. Two of his four-pointers from close range featured dancing feet and will, while Walsh sent him over for the other.
Tabuai-Fidow's 90m runaway try kickstarted the Dolphins' four tries in 15 minutes. Star half Katoa was heavily involved in the tries to Connelly Lemuelu and Jamayne Isaako.
Cobbo raced backwards to scoop a loose pass up effortlessly and dispatch it to centre Herbie Farnworth who raced 30m to put an exclamation point on an extraordinary half of footy.
Katoa's incredible chip kick after halftime for Lemuelu levelled it up at 30.
A Walsh penalty goal restored Brisbane's advantage before Tabuai-Fidow leapt above the Broncos fullback with sheer genius and Cobbo landed the knockout blow.
The Dolphins' bench was enormous and helped turned the tide. The sight of pocket rocket Max Plath carrying three Broncos on his back defied physics.
Ball-playing lock Kurt Donoghoe was crafty and tough in the halves to help secure his side's seventh win in a row at the venue.
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