Again the scrum led to the fifth penalty of the game, which Halfpenny despatched, but Leali’ifano tied matters up again three minutes before the break after Dan Lydiate was penalized for offside.
Halfpenny still had time to send the Lions into the break with a 12-9 lead when Ben Mowen transgressed at the breakdown and the Welshman slotted the ball through the posts from wide.
There was little more cohesion in the scoreless first 15 minutes of the second half, but the Lions looked more and more comfortable and the Wallabies increasingly desperate.
Lions winger George North summed up the physical effort of the tourists when being tackled by his opposite number Israel Folau on the hour mark, hoisting the former rugby league international into the air and driving him backwards.
By now the Lions were dominating the scrum and James Slipper was penalized at the next set piece, Halfpenny keeping his cool to punish the replacement prop and give his side a 15-9 lead after 63 minutes.
The Wallabies charged back and won a penalty close to the try line in the 72nd minute, but Horwill chose to take a scrum and when the ball came out Folau lost it in midfield.
They only needed to get it right once, though, and that moment came after a period of prolonged pressure when Genia spotted a thin defensive line to the left and flyhalf James O’Connor got the ball to Ashley-Cooper who dived over.
It only remained for Leali’ifano, perfect with four kicks from four place kicks on the night, to curl the conversion through the posts, giving his team the lead for the first time.