Trailing at the end of the second and third quarters, the Lions kicked five goals to one in the fourth term to claim a hard-fought 16.14 (110) to 14.9 (93) win on Saturday night.
It's the first time since round nine the Lions have won back-to-back games and they return to third spot, two points clear of Fremantle after the Dockers' draw with Richmond on Friday night.
"The game could have gone any way at three-quarter time and I thought our players showed really good composure and calmness," Lions coach Chris Fagan said.
"They played together as a team in the last quarter. No-one tried to win it off his own boot or anything like that. It was all all done in the right way.
"We stood up to a good pressure test, I reckon, in that quarter."
Joe Daniher and Charlie Cameron kicked three goals each for the Lions, with Rhys Mathieson and Lincoln McCarthy managing two majors apiece.
For the Suns, Levi Casboult finished with four goals while debutant Elijah Hollands kicked two as did Mabior Chol and Brandon Ellis.
Touk Miller was a standout with a game-high 34 disposals, seven tackles and four clearances to win the Marcus Ashcroft Medal as best-on-ground for a third time.
Brisbane star Lachie Neale had 32 touches and 10 clearances in a typically all-action display for the Lions while defender Brandon Starcevich and midfielder Hugh McCluggage were also impressive.
"Look, our boys had a go, we're really proud of that," Suns coach Stuart Dew said after an eighth straight loss to the Lions.
"Brisbane are a quality side. Very clinical. They don't give you any easy ones. We gave them quite a few easy ones.Â
"We've really got to tidy up on that and keep working on that but in terms of physically where we've been in these clashes before, we made a real note to not get beaten in that area.
"I feel like we didn't. It just didn't translate to the scoreboard."
The hosts made a fast start when Daniher and Cameron both scored early goals but Hollands' goal with his first touch in AFL football sparked the Suns.
Cameron's second meant Brisbane held an eight-point lead at the first turn before the Suns took control in the second quarter on the back of inspirational work by Miller.
Hollands mixed the good with the bad, taking a defensive mark before his kick near the goal square was smothered by Daniher, who slotted his second.
It was all Suns after that, with the visitors kicking three unanswered including one to David Swallow in his record-breaking 193rd appearance for the club to hit the front for the first time in the game.
When Hollands' kicked the second of his debut match, the Suns were seven points clear and held onto a goal lead at the main break.
A thrilling third quarter featured a number of lead changes as both teams kicked five goals each, Chol's second of the night seconds before the siren putting the Suns seven points clear at the final turn.
Daniher's third early in the final quarter, breaking an Ellis tackle, levelled the scores again before the Lions kicked clear to secure the win.
The Lions travel to Melbourne to take on Richmond next weekend while the Suns host West Coast at Metricon Stadium.
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