A try from fly-half Jonathan Sexton - and another Leigh Halfpenny conversion - put the Lions clear again heading into the final quarter.
Sexton touched down after receiving the final pass from Halfpenny in a slick Lions move in the left corner.
Australia had closed the gap to just three points early in the second half through two Christian Leali'ifano penalties.
Halfpenny added another penalty of his own.
More top news
A generally dry and mild night with showers confined to inland areas. A few mist patches are likely by the early hours!
After weeks of doubt, Joe Ledley has been included in Wales' twenty-three-man squad for next month's Euro 2016 finals.
Hundreds of fans have signed a petition calling for football fanzones in Wales so supporters at home can share in the atmosphere.