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
The Welsh Government will later launch new plans to reduce the number of children living in poverty in Wales.
Plaid Cymru are to launch their campaign this morning ahead of May's general election.
A study by Swansea University has found a fifth of students in the UK have considered working in the sex industry to fund their studies.