With Rhys Priestland, another player maturing at international level at high speed, and Leigh Halfpenny adding the remaining points with the boot, Wales reached the final four stage for the first time since 1987.
"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," said Warburton.
Wales were never behind after Williams' 56th try for his country inside the opening few minutes, and Warburton claimed making a quick start had been a focus of their preparations.
"We always say we don't start good enough, and we started perfectly today 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.
"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."
Try scorer Phillips added: "It's an historic win, the boys have been outstanding in the lead up to this game. We have so much respect for the Irish boys and I feel sorry for them. They are great players and outstanding gentlemen but we were superb today."
Ireland hit back with a try from Keith Earls and five points from Ronan O'Gara's boot but they were almost always chasing the game and defeat signals the end of the World Cup road for the likes of O'Gara, Paul O'Connell and captain Brian O'Driscoll.
O'Driscoll said: "We got outplayed in the second half, they scored two good tries, maybe there was some weak defence but we are very disappointed to be going home.
"It was a great opportunity after winning the group but they proved worthy semi-finalists and good luck to them.
"We needed to deliver a performance similar to against Australia or Italy last week, but we didn't, we knocked on too much ball and when you turn too much ball over against quality of opposition they make you pay and we are the ones left disappointed."