The Dolphins fought back from a 10-point deficit at halftime to lead 16-14 with 12 minutes to go on Saturday night when Cobbo showcased the rare talent that he is.
The 21-year-old ran backwards to collect an errant pass near the sideline before chipping the ball ahead from 25 metres out.
Cobbo ran around Dolphins defenders to retrieve the ball, kept his elbow up off the ground as he neared the line and score one of the best individual tries of the NRL season.
He iced the cake with a late dart down the sideline to score his third for the night and break Dolphins hearts.
"Selwyn had a terrific game," Broncos coach Kevin Walters said.
"We know what Selwyn brings to our footy team. We haven't seen a lot of it this year for different reasons.
"His hip was giving him some grief, but it's the freest he's run on the field and we're just really happy he's on our side."
The Gabba had not hosted a rugby league game since Australia played New Zealand in 1956.
The sold-out crowd of 30,606 was treated to a 'Battle of Brisbane' thriller.
The Dolphins had an early Hamiso Tabuai-Fidow try disallowed due to an obstruction on Brisbane captain Adam Reynolds and the Broncos soon found their groove.
Cobbo streaked past opposite number Tesi Niu to score. Halves Reynolds and Ezra Mam then combined to send centre Herbie Farnworth in to give the Broncos a 10-nil lead in the 22nd minute.
The presence of Tabuai-Fidow in the centres had Brisbane centre Kotoni Staggs second guessing himself in defence and the Dolphins responded superbly with a right-to-left movement that sent Kodi Nikorima over.
Farnworth crashed through again off a Mam pass and at halftime the Broncos appeared in control with a 16-6 lead.
The Dolphins suffered a major blow when veteran forward Felise Kaufusi failed a head injury assessment in the 17th minute but they refused to relent.
Blockbusting Dolphins centre Valynce Te Whare crashed over three Broncos defenders to narrow the deficit to four points after the break and it was game on.
The Dolphins started to find their mojo and Brisbane faded under the onlsaught.
Hooker Jeremy Marshall-King darted over from dummy-half to give the Dolphins a 16-14 lead in the 63rd minute and an upset was on the cards.
Cobbo turned the game and made sure the Broncos (12-5) moved back to second spot on the ladder.
The Dolphins (7-9) suffered their fourth consecutive loss and must start winning to have a hope of playing finals.
Coach Wayne Bennett said it was a step in the right direction.
"It was pretty gutsy of them to stay in the game, after the way we played in the last couple of weeks," he said.
"We were very pleased with our effort."
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