"You can't miss an opportunity like that," Italy coach Nick Mallett said.
Immediately after the break, Italy flyhalf Andrea Masi threw a speculative pass that Tom Shanklin, playing in his 50th Test for Wales, intercepted to score. Williams added his brace and Byrne notched his second.
Prop Martin Castrogiovanni scored Italy's sole try.
Flyhalf Ronan O'Gara dictated play for Ireland, who needed a convincing win in Dublin to build upon an improved performance in a 26-21 loss to France two weeks ago.
"It was important that we got a win today," man-of-the-match Geordan Murphy said.
Ireland, who missed out on last season's title only when France scored a last-minute try, scored tries through David Wallace, Rob Kearney, Marcus Horan and Tommy Bowe (two).
Scotland, down 14-3 at halftime, hit back with Chris Paterson's second penalty and a try by Simon Webster, but Ireland produced the try of the match in reply.
Murphy offloaded a looping pass to O'Gara and the flyhalf gathered and flicked the ball under his right arm to Andrew Trimble in one fluid movement. Trimble then drew in the defense before passing inside to Bowe, who just made it across the line despite a last-ditch tackle by Mike Blair.
The tournament resumes in two weeks with Ireland hosting Wales, Scotland taking on England and France welcoming Italy.
RSS