Brisbane was two-up at the break after goals from the clinical Andrija Kaluderovic and an incredulous own goal by Eugene Galekovic, who after last week's heroics had a rare off night for the Reds.
Jack Hingert scored his debut A-League goal to seal the win for the visitor, with Craig Goodwin's strike and a late Pablo Sanchez penalty, after Daniel Bowles was sent off for preventing a scoring opportunity, proving merely consolation.
The win moves Brisbane three points behind Melbourne City in sixth, although it was still play in the finals after Perth Glory was kicked out for salary cap breaches.
Adelaide meanwhile remains in fourth spot after missing its chance to go top with a win.
The weary Roar had to deal with a number of injuries and tiring legs after its AFC Champions League loss in Korea midweek.
Despite its travels it was Brisbane which began the brighter and took the lead on 26 minutes.
Bowles found Jean Carlos Solorzano midway inside the host's half and with his first touch the Costa Rican played a delightful ball through to Kaluderovic.
With only Eugene Galekovic to beat the Serbian striker steadied himself and slotted the ball past the Adelaide shot-stopper to score his fifth goal in eight matches and give Roar a 1-0 lead.
Just before the half hour the visitor had the ball in the net again, but Broich's effort from close range was ruled out for offside, with replays showing it was a very close call.
Adelaide's best chance came minutes later as Bruce Djite used his strength to burst into the area and his shot across goal was touched by Jamie Young onto the post.
It fell perfectly into the path of Craig Goodwin, who from just a metre out somehow hit the side netting.
Brisbane doubled its lead five minutes five before the break in bizarre circumstances.
Galekovic came out of the area to clear, but the goalkeeper misjudged the bounce and as he stuck out a leg it only lifted the ball closer to goal.
As he desperately tried to scramble it away under pressure, Galekovic only managed to steer it into his own net and hand Brisbane a two-goal advantage at the interval.
It took less than 10 minutes for Roar to add to the scoreline in the second half. Jack Hingert found himself with plenty of space deep in Adelaide territory.
He played a simple one-two on the edge of the area with Brandon Borrello and then beat Galekovic on the near post to make it 3-0.
Djite did his best to inspire his side after forcing Young into a manageable, but difficult save moments later.
The Reds gave themselves some hope of a fight back in the 71st minute. A ball over the top had Sergio Cirio sprinting down the right and he delivered a dangerous low cross into the middle.
Goodwin this time made no mistake from close range to pull one back for the home side.
Bowles saw red after bringing down Nigel Boogaard in the box to give Adelaide a penalty deep into stoppage time. Sanchez slotted it past Young but it came too late for the host.
Roar coach Frans Thijssen admitted it made for a nervous ending and was disappointed to lose Bowles for its next game amid a defensive injury crisis.
"It's a bit sad that we get another defender sent off with our injuries in defence - that doesn't help us," Thijssen said.
"I'm very happy with the first half - we made it a little bit difficult for ourselves in the second half after the 3-1 (lead); there was a little bit of panic in the team.
"But we're quite happy with a win here."
Adelaide coach Josep Gombau believed his side lost the game in the first half.
"At this moment of the season... it's important to get a result," he said.
"Everybody knows how important the game is ... maybe we are not used to this (pressure).
"It's part of football, so we need to have this experience if we want to be at the top."
