Sportal.co.nz 30.Jun.2013Getty Images
The Lions led 15-9 after five Leigh Halfpenny penalty goals but the hosts launched a sustained attack and finally cracked the tourists' defence when Ashley-Cooper crossed five minutes from full-time.
James O'Connor, who had a mixed night in the number 10 jumper, straightened the attack and delivered a short ball for Ashley-Cooper to slip between Jonathan Davies and Tommy Bowe.
Christian Lealiifano held his nerve to slot the conversion from the sideline to give the hosts a one-point lead in front of a record 56,771 crowd.
The drama was far from over as the Lions launched the final attacking raid of the game after the siren and earned a penalty for a breakdown infringement leaving Halfpenny the chance to steal victory.
But the Wales sharp-shooter left his 50m attempt well short, with Will Genia booting the ball into the stands to spark wild celebrations in front of the Lions-dominated crowd.
It was a far happier second Test appearance for Lealiifano who kicked a perfect four-from-four with the boot, while Halfpenny produced two rare misses in the narrow loss.
Lealiifano was also among Australia's best in general play while skipper James Horwill and Will Genia also led from the front.
Israel Folau was not as dominant this time around but it was his run that put the Wallabies deep in attack late in the match.
Skipper Sam Warburton was strong for the Lions but limped from the field late with a hamstring injury, while the entire Lions pack were strong as the tourists won the battled of the breakdown.
The result sets up a mouth-watering decider in Sydney next Saturday at ANZ Stadium.
The Lions had the better of the early exchanges and hit the front in the 10th minute when Halfpenny slotted his first penalty goal of the contest to atone for a rare miss in the fourth minute.
The Wallabies won possession from the re-start to and immediately looked to use Folau's aerial skills.
Folau soared above George North to win the ball but Kurtley Beale's kick wasn't deep enough and the Lions escaped without conceding points.
The Wallabies scrum started to dominate as referee Craig Joubert penalised Lions loosehead Mako Vunipola twice for scrum infringements.
Lealiifano converted both penalty attempts in the 17th and 24th minutes to give the hosts a 6-3 advantage.
Vunipola's horror night continued when he grassed a regulation pass just as the Lions were starting to build some momentum.
But Lions tighthead prop Adam Jones provided relief for the tourists, earning the visitors' first scrum penalty, with Halfpenny slotting the long-range attempt to level at six-all.
Vunipola followed Jones' lead, getting the shove on Ben Alexander and winning a penalty which Halfpenny slotted on the half-hour for a 9-6 lead.
The shoot-out continued with Lealiifano slotting his third penalty of the night three minutes from half-time but Halfpenny had the final say of the first stanza to lead 12-9 at the break.