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
Tree pollen levels are easing off now! But beware - grass pollen is just becoming airborne and levels will rise during settled spells.
Northern areas will see a few showers this afternoon - but there'll be plenty of warm sunhine too!
Wales is facing a recruitment shortage for secondary school teachers. At the start of the year a third of training places were not filled.