Twelve years on from their last Test on Australian soil, it took the visitors just 22 seconds to hit the lead.
Joe Schmidt's side then conceded after 10 minutes and scrambled desperately to limit the damage in a thunderous Lions first half.
The lead swelled to 24-5 after 42 minutes before the hosts controlled the contest, late tries to replacements Carlo Tizzano and Tate McDermott restoring order ahead of a must-win Melbourne Test next Saturday.
"Very proud of the way the players fought their way back," Schmidt said.
"A comparatively young side ... still finding their way.
"This time last year we would have melted, but I love the way this team is developing."
Earlier the hosts had looked indecisive and impatient as Brisbane again proved a happy hunting ground for a Lions team unbeaten in the city.
Prop Tadhg Beirne was player of the match while Tadhg Furlong, flyhalf Finn Russell, flanker Tom Curry and prop Ellis Genge were the other tormentors in front of a 52,229-strong Suncorp Stadium crowd, mostly drenched in Lions red.
Beirne and Furlong's selection raised eyebrows in the travelling press.
"I read all that ... (they're) big game players," coach Andy Farrell.
"Immense, absolutely immense ... set the tone, really.
"To get off to a winning start is huge. It puts the pressure on for next week and keeps us in the tour until the last game."
Max Jorgensen scored the Wallabies' only first-half points, spectacularly pinching a Jake Gordon box kick and racing 22 metres to score against the run of play.
The Lions were up 3-0 when Joseph-Aukuso Suaalii was penalised for not releasing with his first touch from the second phase of play and they took the points.
An Australian crossed in the ninth minute, but unfortunately for the Wallabies it was Scottish captain Sione Tuipulotu, who left Melbourne via Japan six years ago and on Saturday became the first Australian-born Lion to play a Test since 1910.
The centre was involved again soon after, shifting the ball left before James Lowe palmed off Jorgensen and set up Huw Jones.
Jones' try was disallowed though, replays showing Jorgensen had a hold of Jones' leg when he attempted to play on and score.
Tom Curry barged over before halftime in a blow for the desperate Wallabies, who had scrambled so well to limit the damage.
There was no respite though, the Lions finding open spaces almost from kick-off before Dan Sheehan touched down in the right corner for a 24-5 lead.
Any faint hopes of a comeback were extinguished when Suaalii was denied what had been initially adjudged a try when he'd rolled over the line without releasing the ball.
They really knew it wasn't their night when captain Harry Wilson's neat in-behind grubber kick took a nasty turn just as winger Harry Potter was poised to score an opportunistic try.
Tom Lynagh was brave and busy in 60 minutes in his first Test start, taking on the line, reacting calmly, mopping up and getting hammered in the air by Curry while catching a bomb.
Curry escaped a card for that offence, just as Furlong did despite making high contact on Suaalii in the ruck.
Schmidt said he was satisfied with both decisions, happy for officials not to "go looking" for yellow cards.
A sharper final 30 minutes will give Schmidt plenty to ponder ahead of Melbourne, the coach confirming on Saturday night that crucial pair Rob Valetini and Will Skelton will be fully recovered from calf niggles.
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