The Lions ran in four tries at the ANZ Stadium as they triumphed on tour for the first time since 1997's trip to South Africa.
© PA Photos
Halfpenny extended his side's advantage with a penalty on 10 minutes, but the Wallabies got off the mark soon after thanks to Christian Lealiifano's kick.
However, three more penalties from the impressive Halfpenny saw the Lions open up a 19-3 lead with 26 minutes on the clock.
© PA Photos
The tourists looked to be in total control of the contest thanks to some dominant scrummaging, but Australia scored their first try of the match on the stroke of half time as James O'Connor showed some quick feet before going over. Lealiifano made no problem converting as the Lions took a 19-10 lead into the break.
The hosts carried their momentum into the start of the second half as two quick Lealiifano penalties reduced the deficit to three points.
Another kick from Halfpenny on 52 minutes kept the scoreboard ticking over for the Lions and they landed a significant blow around the hour as Jonny Sexton touched down in the corner before Halfpenny added the extras.
Australia continued to put the pressure on their opponents, but it was the Lions who scored another try in the 65th minute when Halpenny made a blistering run through the home defence before offloading for George North to finish.
The victory was sealed with 10 minutes to play as Jamie Roberts burst through to score, allowing Halfpenny to convert.