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
There are concerns mounting over a plant growing out of hand across Wales which is devaluing properties by half.
Getting fresher and brighter in the north this afternoon
A cloudy night with some showers but becoming drier in the early hours