Wales wing Alex Cuthbert's two second-half tries proved decisive in a match they had to win by seven points to retain the title for the first time since 1979, provided they maintained their superior try-count.
As it was the defending Grand Slam champions beat a 108-year-old record to clinch their biggest win over England, surpassing the 25-point margin recorded in a 25-0 win back in 1905.
"It's unreal, it's what dreams are all about," said Wales flanker Justin Tipuric, who was named man of the match.
"We were outstanding, we all worked so hard, it's brilliant. We knew what we could do, we talked about it all week and we were ready to play since Monday."
Tipuric said Wales's opening defeat at the hands of Ireland had inspired them to their victory.
"We got a lot of bad media. That gave us a kick up the backside, but we all stayed tight."
England coach Stuart Lancaster admitted Wales had been the better side.
"We are gutted. We didn't get the execution right and didn't turn up," he said.
"We just weren't good enough. We have no complaints, we couldn't match their physicality."
After building a 12-3 lead early in the second half, through four penalties by full-back Leigh Halfpenny to one from England fly-half Owen Farrell, Wales surged ahead through a try by Cuthbert.
That put them 17-3 in front and minutes later Farrell missed his second penalty in three attempts.
Dan Biggar added a drop-goal before Cuthbert stormed in for another try, with fly-half Biggar completing the rout with a penalty.
This was Wales's second victory in a row over England, with the Welsh the only side to defeat the English in Six Nations action since Lancaster became coach of the Red Rose brigade in 2012.
Earlier, Italy produced a breathtaking display to hand Ireland a 22-15 defeat on what was Andrea Lo Cicero's 103rd and final appearance for the Azzurri and possibly Brian O'Driscoll's last game in an Irish shirt.
Italy had started this campaign with a 23-18 victory over France and after defeats to Scotland, England and Wales ended it with another deserved win over one of the pre-tournament favourites.
It was Italy's fourth win over the Irish but first in the Six Nations.
Italy have now won twice in the Six Nations for only the second time, the last being in 2007.
Ireland, meanwhile, are in danger of picking up their first ever Six Nations wooden spoon if results elsewhere conspire against them.
Despite an opening win against Wales, coach Declan Kidney fell under pressure after defeats to Scotland and England and then a draw against France last week.
Ireland, missing injured fly-half Jonathan Sexton, had the early momentum and Paddy Jackson put the first of his 15 points on the board with a sixth-minute penalty after Leonardo Ghiraldini was whistled for a tackle on Conor Murray.
However the visitors' luck soon ran out in a half which saw several of their players come off injured and iconic centre O'Driscoll sent to the sin-bin.
Ireland went in at the interval 9-6 down and without winger Keith Earls and Luke Marshall, both of whom were injured.
Italy had Ireland on the ropes in the opening few minutes of the second half and were finally rewarded with the only try of the game thanks to Gio Venditti, who squeezed the ball over on the right.
Orquera, from 35 metres out, converted to give Italy a 16-6 lead.
Ireland came fighting back and cut the deficit through two successive Jackson penalties to take the score to 16-12 just before the hour and, with Parisse sin-binned, came close to making the breakthrough after a dominant 20-phase spell in which they finally had to settle for another Jackson penalty.
Parisse returned as a tearful Lo Cicero ended his Italy career to a standing ovation, but Italy spurned another chance to extend their lead when Garcia's penalty effort was short and wide.
When Orquera was restored to kicking duties minutes later he sent Italy 19-15 in front.
Ireland were further penalised when Conor Murray was sin-binned for a tripping offence.
Italy won yet another lineout and a subsequent penalty, with Orquera sealing victory in the final minute.