While Hannant impressed after being injected into the starting side, all of Brisbane's big guns fired - particularly lock Corey Parker - to quickly have the visitors over a barrel.
Brisbane led 16-6 at halftime despite alarm bells sounding early for the embattled hosts when fullback James Tedesco pounced on a clever grubber from another to return from Wests Tigers' injury list - Liam Fulton - to score in just the fourth minute.
Then it was all one way traffic.
Justin Hodges (56th minute), Scott Prince (66th) and Josh Hoffman (79th) crossed, the procession only interrupted by Wests Tigers' Sauaso Sue (76th).
The omens were bad for Wests Tigers early on - lock Braith Anasta came off in the 10th minute with a suspected shoulder injury and hooker Masada Iosefa was placed on report in the 26th for sliding his knees into Sam Thaiday.
Iosefa was also denied a 33rd minute try for obstruction.
Parker was outstanding, finishing with 184m, 31 tackles and eight offloads in a performance that should earn him a Queensland starting backrow spot for game two on June 26.
And Hannant (194m, 31 tackles) would have made Queensland selectors sit up and take notice.
But Broncos skipper Sam Thaiday surprisingly did not back Hannant's immediate Origin return.
"Let him play a few games for the Broncos first. I really think personally he needs to prove himself here," he said.
"He's getting older, getting a few niggling injuries. But that is not my decision."
Griffin said it wasn't the much needed win but the way they earned it that had provided relief.
"What we got out of tonight wasn't the scoreline. It was how we worked hard for each other," he said.
Meanwhile, Wests Tigers coach Michael Potter had injury added to insult with Anasta (shoulder) expected to miss "two to three weeks".
"With the press they have copped and their backs to the wall attitude ... they were more desperate than us," he said of the Broncos.
- AAP
