The Lions, with tries from George North and Alex Cuthbert, led 23-21 with the clock ticking into the 80th minute when Australia replacement Kurtley Beale fell short with a 46-metre penalty. As the ball bounced dead, the final whistle signalled a winning start to the series for the tourists.
Tigers duo Tom Youngs and Tom Croft – in his second Lions tour – started the game for the Lions and they were joined by second-half replacements Ben Youngs, Dan Cole and Geoff Parling.
Australia claimed a seven-point lead after less than quarter of an hour, with Will Genia providing the break and the opening for wing Israel Folau to run in on the right. James O’Connor added the conversion after missing two earlier penalties.
Full-back Leigh Halfpenny got the Lions on the board with a penalty and just two minutes later Welsh wing North provided a solo score to put the tourists in front for the first time.
North fielded a kick from Berrick Barnes on the Lions 10-metre line and burst through before beating Genia into left corner. Halfpenny converted from touchline to make it 10-7.
When North was denied a second score by the TMO, confirming his left elbow had nudged the touchline a fraction ahead of placing the ball over the tryline, Halfpenny provided consolation with a penalty to provide a six-point lead.
The reply was instant from the hosts with Folau stepping his way into the right corner for his second try.
It was still 13-12 to the Lions at half-time before Cuthbert made a big break through midfield and shrugged off four tacklers to score. Halfpenny’s conversion took the lead to eight points at 20-12.
But Australia were not done yet, despite being forced into a reshuffle in the backline after injuries to Christian Leali’Ifano, Berrick Barnes, Pat McCabe and then Adam Ashley-Cooper, meaning a move to centre for flanker Michael Hooper and a role on the wing for replacement scrum-half Nick Phipps.
O’Connor kicked a penalty to pull it back to 15-20 and replacement Beale provided a tense closing 20 minutes when he landed a kick to make it 18-20.
Cole was on the field for the last half-hour, Ben Youngs arrived just after the hour mark and joined brother Tom on the field for a couple of minutes before the hooker was withdrawn after a typically industrious afternoon's work.
Halfpenny got on the mark again with a penalty after 65 minutes but the Lions were pegged back once more as Beale made a sharp break up towards the tryline and, when the tourists were whistled at the breakdown, the penalty brought it back to 21-23.
Parling came into the second row for the last 10 minutes, with Croft being replaced by Dan Lydiate for the final seven minutes of a rollercoaster match.
The final twist came after Beale scooped a kick wide on 74 minutes and then, with nerves fraying in both teams and among both sets of supporters, Australia were given a penalty at a Lions scrum with around 90 seconds remaining.
Beale lined up the kick but, as he looked to give it an extra push from 46 metres, he lost his footing and saw the ball fall short and bounce dead as the referee blew for full-time.