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
Two men who took part in a terrifying robbery at a rural store near Mold – when staff were threatened with a large machete - are jailed.
From the HTV Cymru archives here's the 1969 hit by legendary singing duo Toni ac Aloma singing about a village cafe on Anglesey.
The whale was rescued last week and helped back into the sea. Environmentalists "sad" to find it had subsequently died.