France can successfully retain the title by beating Scotland at Murrayfield on Saturday.
While Ireland won their first-ever Friday home championship match with a four-try bonus point, Wales took most of the plaudits.
Wales started as 20-point underdogs but trailed by only two as late as the 68th minute.
Wales hadn't beaten Ireland in Dublin in the championship in 14 years, but Irish flyhalf Jack Crowley was made to kick a 77th-minute penalty to avoid the chance of a humbling draw.
Wales were second best in terms of territory and possession but backed up their three-point home loss to Scotland in the last round with magnificent defence, and an even better all-round show of commitment and progress.
Wales' Six Nations losing streak was extended to 15 games and they may yet finish the tournament with a third consecutive wooden spoon, but they were more encouragingly competitive against Ireland than coach Steve Tandy hoped for.
"We're disappointed but massive pride in our character," Tandy said. "There's confidence building in the team and that is going to take us to the win in the near future."
There was none of the fist-pumping joy by Ireland coach Andy Farrell during the record away win against England two weeks ago as his team failed to back that up with the expected big win over Wales.
"Credit to Wales, they were outstanding, certainly getting better defensively," he told broadcaster ITV. "They made it a scrap so to come away with a bonus-point, happy with that."
Wales' rush defence, spearheaded by centre Eddie James, was outstanding, especially on the tryline. Alex Mann made 28 tackles and two turnovers in his 22, Dafydd Jenkins added 27 tackles, James Botham 24 and Dewi Lake 23.
Ireland winger Jacob Stockdale ran off the shoulder of midfielder Stuart McCloskey to score his first Test try since 2021.
Holding out Ireland galvanised Wales.
Ireland took a half-hour to score again, through Crowley, who couldn't convert his own try.
The Irish looked set to reach half-time up 12-3, but Wales prop Rhys Carre made like a winger from 35 metres out and blew past three Irish for a brilliant try.
"I saw some space and went as hard as I could and no one caught me," Carre told ITV.
The Irish gave themselves breathing room on the scoreboard again when Jack Conan scored from a tap penalty after half-time.
But Wales refused to bow. Josh Adams botched a try chance throwing a forward pass to Botham but Botham scored off a ruck and Dan Edwards converted to make it 19-17.
It took a Joe McCarthy steal to launch the fourth Irish try walked in by fullback Jamie Osborne with 12 minutes to go. Crowley, who missed two easy goalkicks, made the result safe for Ireland with his only penalty.
25°C