Jonathan Davies wrapped up a semi-final spot with a try just after the hour mark and Rhys Priestland kicked seven points to send Ireland home.
And after reaching the last four for the first time since 1987, Warburton set his sights on eclipsing the achievements of 24 years ago.
"The team in 1987 did it (reached the last four) and got third place. But we have the semi next week, the boys are thrilled and it's a massive achievement, it's brilliant," he said.
"It was a massive performance, we knew they had a lot of big ball carriers and there was a lot of tackling stopping them on the gain line because they are dangerous, it was a fantastic defensive effort.
"We always say we don't start good enough, and we started perfectly and it was just what we wanted. It's easier to be ahead of the game than chasing it. It's a massive achievement and we have worked so hard."
Wales flew out of the traps and scored the game's first try inside three minutes when Williams dived in at the corner after Jamie Roberts collected Priestland's high kick and No.8 Toby Faletau barged through the Irish defence.
Priestland converted before Ireland turned down three kicks a goal in an attempt to gain the converted score which would bring them instant parity only for Wales' ferocious defence, led by skipper Warburton to keep them out.
Ronan O'Gara eventually reduced the lead by three points with a penalty in front of the posts only for Leigh Halfpenny to again extend the gap with a mammoth three points.
Ireland coach Declan Kidney whipped up his troops at the break and four minutes after the restart they were level on the scoreboard after Earls snuck in at the corner and O'Gara converted.
The lead was short lived though and five minutes later Wales scrum-half Phillips, scorer of a controversial try when the two sides met during this year's RBS 6 Nations, flew over the whitewash to put Warren Gatland's side 15-10 ahead.
And after working so hard to get back into the contest Ireland's hopes were dealt a terminal blow when powder-puff tackling allowed centre Davies to wander over the try line with 15 minutes left.
Priestland rediscovered his poise to convert from the touchline, leaving Ireland with a 12-point deficit they never reduced and sending Wales marching into the semi-finals.
"We got outplayed in the second half," said Ireland captain Brian O'Driscoll. "They got two good tries in the second half, maybe some weak defence from us, but I am desperately disappointed to be going home. But Wales were tremendous and are worthy semi-finallists.
"We needed to produce a performance like we did in the Australia game, or even in the Italy game. But we knocked on, lost too much ball, and against good opposition they make you pay."