Ireland led 20-10 when fellow Lion Paul O'Connell had dotted down before O'Brien's first try.
Scores from Jared Payne and another from O'Brien then took Ireland beyond the grasp of their hosts.
"I think we did all we could do out there," said O'Brien. "We stuck to our guns and got the result.
"Driving into this ground with all this Irish support, it was great to have so many here."
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