Former Irish skipper O’Driscoll was among the try-scorers as Declan Kidney’s side gained a measure of revenge on the Welsh for a series of defeats in the championship.
“The first game is a must-win,” O’Driscoll said. “Otherwise you are chasing your tail for the rest of the championship. We started really well today.”
Ireland led 23-3 at half-time, thanks to converted tries from Simon Zebo and Cian Healy, as well as three Jonny Sexton penalties. Wales had only mustered a solitary penalty through Leigh Halfpenny.
O’Driscoll added to his side’s lead before Wales fought back with scores from Alex Cuthbert, Halfpenny and replacement Craig Mitchell, but the visitors held on.
O’Driscoll, who lost the captaincy to Jamie Heaslip before the tournament, added: “We started really well — we owed Wales one, they’ve done a job on us the last three times.”