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.
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Sunny spells during the evening with isolated showers easing away, although it will cool off quite quickly.