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
Rain moving east, will spread across Wales in the first half of the night, some likely heavy.
Rain moving east, heavy at times
The Lesbian, Gay, Bisexual and Transgendered communities in Cardiff are celebrating 30 years of campaigning; as part of LGBT History Month.