The Raiders had their chances but lacked execution and constantly pushed one too many passes.
Brisbane's Jack Reed marked dangerous Raiders centre Jack Wighton superbly, copping a head knock for his efforts yet returning after concussion tests.
The Raiders survived several early scares, holding their opposition scoreless for the opening 20 minutes for just the third time this season.
But the Broncos were on the board just three minutes later when a half-break from Maroons centre Justin Hodges resulted in Copley scoring in the corner for his 10th try of the season.
The Raiders struggled under the high ball throughout the night, in particular winger Reece Robinson, and it wasn't long before Copley swooped on his crumbs to bag a second and give the Broncos a 12-0 lead into the break.
The opening exchanges of the second half were fiery, Raiders forward Paul Vaughan and Josh McGuire both put on report within three minutes of play resuming for dangerous tackles.
Robinson then fumbled another high ball and McGuire slipped through the Raiders' defence for an 18-0 lead.
McGuire was in the thick of it again when he was placed on report for a second time for a late hit on Milford.
Lock Shaun Fensom finally got the Raiders on the board when he scrambled over in the 69th minute, but the missed conversion attempt and tries to Ben Barba and Alex Glenn crushed any hopes of a comeback.
The Raiders confirmed after the match that Papalii would miss three to four weeks, ruling him out of Origin two.
"Injuries happen, you just have to deal with it and see how you bounce back," Papalii said.
Raiders coach Ricky Stuart was frustrated that his side wasn't getting "rewarded for their efforts".
He was also left lamenting missed catches under the high ball.
"One missed tackle, and two dropped bombs and we're 18 points behind," he said.
"We're just doing the little things wrong at the moment.
"And little things in this game add up to big results."
It was Brisbane's fifth win in-a-row on the road, and Broncos co-captain Justin Hodges praised his side's goal line defence.
"It was outstanding," he said.
"There were times there in the first half where they had three sets back-to-back.
"They threw everything at us there and our main goal tonight was for just everyone to turn up for each other."
- AAP