Their duel in the centres was the week's talking point after the pair's form saw them surge into NSW State of Origin contention.
But it was the Broncos firebrand who left Suncorp Stadium on Thursday night with the upper hand, smothering the rampaging Talakai and scoring a brilliant try of his own.
Victory burst the Sharks' bubble as they fell to 5-3, while Brisbane (4-4) will spend the night nestled inside the top eight on the live ladder.
The win came after Adam Reynolds copped a stray elbow to the nose in the 34th minute, the Broncos skipper returning for the second half stitched up after passing his head injury assessment.
Carrying a shoulder injury, Payne Haas played through obvious discomfort in the first half and didn't take a break until there were 25 minutes to play.
Staggs stopped Talakai in a one-on-one tackle just five metres from the line and twice forced turnovers on his opposite man.
But Talakai was not alone in his fumbles.
The Sharks looked slick in the first half but lacked polish at the pointy end of their sets, completing just 11 of their first 17.
It meant they missed their chance to build a lead, five-eighth Matt Moylan's grubber kick to himself their only try of the half.
Brisbane found a reply soon after Reynolds' exit, the impressive Tyson Gamble and Te Maire Martin going right to a rampaging Staggs who dummied and left both Talakai and Ronaldo Mulitalo in his dust.
Staggs then converted his own try from the sideline before Nicho Hynes slotted a field goal to send the Sharks to the sheds ahead 7-6.
The errors remained for the visitors after the break, another allowing Brisbane to strike early when Herbie Farnworth busted over off another Gamble pass.
Corey Oates then broke the line but couldn't find support, Kurt Capewell ensuring the points came later in the set when he stepped out of a tackle and stretched over the line.
Twice Farnworth broke free but didn't pass to his winger Oates, while Reynolds missed a golden chance to seal the result when he dropped a Rhys Kennedy inside flick pass with the line begging.
But it mattered little as their often flimsy defence held firm.
Sharks fullback Will Kennedy was one of his side's best while Cameron McInnes was placed on report for a crusher tackle on Staggs.
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