O'Driscoll and co put their stamp on the match early, were well in charge by half-time and not hard-pressed to withstand belated Welsh resistance which resulted in two tries for replacement wing Tom Shanklin.
Ireland were immediately in charge thanks to RBS Man of the Match Byrne's first-minute try.
He took Wales unawares by breaking free from a rolling maul and charging over completely unattended from close range.
Ronan O'Gara converted - but within five minutes a Stephen Jones penalty got Wales on the board too.
By the quarter-hour, though, sustained Irish pressure was rewarded with a second try.
Centre O'Driscoll jinked and muscled his way over, and O'Gara once again converted.
Both teams were contributing to an entertaining spectacle of running rugby - and Ireland had to be alert to cover Wales breaks through the backs.
O'Gara was wide with a penalty attempt from close on 50 metres, and Tyrone Howe was kept out only by a last-ditch tackle by Martyn Williams as Ireland threatened to move out of sight midway through the first half.
But by the half-hour the hosts were 19-3 in front, after O'Gara had charged down an attempted clearance from Iestyn Harris and chased over the try-line to touch down.
The Munster stand-off was unable to convert, but Wales were already in danger of being swamped.
Both sides had to make changes before the break, Welsh prop Adam Jones replaced by Gethin Jenkins and Malcolm O'Kelly brought into the hosts' second row for Donncha O'Callaghan.
Just when it looked as if Wales may turn around still just about within sight of their opponents Byrne popped up with his second try of the match.
Proving a more than able replacement for retired Ireland lynchpin Keith Wood, he went in at the corner this time for his third touchdown in 26 Tests. O'Gara failed to add the extras from wide out, but Ireland were still 24-3 to the good.
Wales had the wind behind them in the second half but rarely threatened to make it count, and instead it was number eight Anthony Foley who collected a short reverse pass from Peter Stringer to extend the Irish lead. O'Gara missed the conversion from a favourable position - but Wales were down and out anyway.
Flanker Keith Gleeson proved the point with a decisive break through Welsh cover, and O'Driscoll was once again the glory boy with the touchdown before O'Gara landed the extras to boot.
Centre Gordon D'Arcy had been at the centre of much of Ireland's best play, but they lost him just before the hour when he limped off to be replaced by Bath's Kevin Maggs.
Wales finally awoke from their slumber with an increased share of possession from their forwards and some spirited running from the backs which culminated in an unconverted try in the corner for Shanklin.
But notwithstanding plenty of late pressure - and a spell in the sin-bin for home full-back Girvan Dempsey - the fightback amounted only to a second Shanklin try.
Jones managed to convert from under the posts, but it was still a hugely disappointing afternoon for the Welsh renaissance theorists.