Australian fly-half James O'Connor finished a jinking run with a try in the very last play of the first half, to narrow the scoreline to 19-10.
The Lions lead at the break thanks to Alex Corbisiero's early try, and 14 points from the boot of Leigh Halfpenny.
Australia could have been ahead, but turned down five opportunities to kick penalties for goal in the first period.
More top news
The First Minister has launched a challenge at the National Eisteddfod today to encourage more young people to start their own business.
The Welsh Conservatives are calling for the Visit Wales tourism organisation to be scrapped, describing it as 'risk averse'.
A Chief Medical Officer is urging young people in Wales to have a new meningitis vaccine that's being introduced today.