Welsh wings George North and Alex Cuthbert scored the key tries for tourists.
British & Irish Lions draw first blood in Australia Tests
Australia 21 Lions 23
Australia Tries: Folau (2), Con: O'Connor Pens: O'Connor, Beale (2)
Lions Tries: North, Cuthbert Cons: Halfpenny (2) Pens: Halfpenny (3)
Wales wings George North and Alex Cuthbert scored tries in each half as they inspired the British & Irish Lions to a pulsating first Test triumph at Suncorp Stadium.
North's breathtaking 60-metre solo effort will go down as one of the great Lions touchdowns, while Cuthbert pounced early in the second period.
A game of brutal intensity saw three Australian players - centre Christian Leali'ifano, full-back Berrick Barnes and substitute Pat McCabe - carried off, which meant openside flanker Michael Hooper playing the final 30 minutes in midfield.
But the Wallabies, mainly through a brilliant try double from debutant wing Israel Folau pushed the Lions to the limit, and they would have won if replacement full-back Kurtley Beale had kicked just one of two late penalties, the second falling short after he slipped at the key moment.
Australia were ultimately punished for their goal-kicking lapses - 14 points went begging from the boot - as Beale and James O'Connor struggled for consistency.
In contrast, though, Lions full-back Leigh Halfpenny landed five out of six shots, and the tourists now head to Melbourne knowing that victory next Saturday would give them a first Test series triumph since they toppled South Africa 16 years ago.
It was the Lions' eighth successive Test victory in Brisbane, and they also appeared to emerge unscathed in terms of injuries, unlike their opponents.
The Wallabies suffered an immediate blow when Lealiifano was knocked out after he attempted a tackle on his opposite number Jonathan Davies.
Davies immediately called for play to be stopped, and Leali'ifano saw his Test debut ended inside the opening minute as McCabe replaced him.
O'Connor then missed two penalties in quick succession for Australia, but after the Lions enjoyed a concerted spell of pressure, they were undone in spectacular fashion.
Scrum-half Will Genia made it all possible when he embarked on a weaving 50-metre run that left his opposite number Mike Phillips in all kinds of defensive strife.
And when Genia kicked into space, Folau marked his Test debut by producing a trademark finish that underlined why Wallabies coach Robbie Deans wasted little time selecting him following his switch from rugby league.
O'Connor added the conversion, but Halfpenny opened the Lions' account before North conjured his moment of magic.
Gathering Barnes' kick 10 metres inside his own half, he then set off on a remarkable run that saw him beat three defenders before showboating in Genia's face and touching down for one of the great Lions tries.
Halfpenny converted and kicked a penalty to hoist the Lions six points clear, and it could have been worse for Australia when North went flat out for a second try, but Folau got his hand underneath the ball.
And Folau then pounced for his second try when he cut inside Sexton and handed off Lions prop Alex Corbisiero for another devastating finish.
O'Connor could not convert, though, as his goal-kicking proved way short of Halfpenny's standard, and there was another blow for Australia when Folau and Barnes clashed heads, resulting in Barnes following Lealiifano in being carried off.
It meant an appearance for Beale, who was back in the Wallabies' Test 23 following his much-publicised problems with alcohol, before Halfpenny missed a penalty - only his second failure from 27 shots at goal - and the Lions trooped off 13-12 ahead.
McCabe's exit early in the second period caused more disruption for Australia, and the Lions capitalised immediately when strong-running Cuthbert powered over on an angled 35-metre run.
It was an outstanding finish by the Cardiff Blues predator, who has scored nine tries in 18 Tests for Wales, and Halfpenny's conversion secured an eight-point advantage.
O'Connor responded by kicking a 51st-minute penalty, yet the Wallabies' injury curse struck again when McCabe departed nursing a neck injury as problems mounted for Australia coach Robbie Deans ahead of next Saturday's second Test in Melbourne.
Beale and Halfpenny then exchanged penalties, making it 23-18, before Beale landed another three-pointer after he ran deep into Lions' territory, setting up a gripping final 12 minutes.
Mako Vunipola conceded a penalty five minutes from time that threatened to give Australia a lifeline, but Beale sent his kick spiralling wide and the tourists escaped, and he missed again with the game's final slice of action from almost halfway, slipping as he made contact with the ball, meaning the Lions could celebrate.