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
Catch up online with Wales This Week, Gleision - The Inside Story
The Cardiff Embankment scheme will stretch from the city centre down Dumballs Road to The Bay. The plans go before the council this week.