The defeat leaves Chris Robshaw's side facing the threat of an early departure from the tournament as they are yet to face Australia.
Twice England jumped out to a 10 point lead thanks to their superiority at the set-piece and the boot of fly half Owen Farrell but Sam Warburton's troops refused to thrown in the towel.
All week leading up to the game all the talk focused on England's selection with Stuart Lancaster picking rugby league convert Sam Burgess in midfield and opting for Farrell in front of George Ford at fly half. However it was Wales' No 10 Dan Biggar who proved the match winner with his faultless kicking in a man of the match performance.
The Ospreys fly half radar was flawless throughout and his cool head in the furnace kept Wales in the game. He managed to keep Wales clinging on as England threatened to batter their way to victory.
Out of nowhere, Wales produced a moment of magic when replacement scrum half Lloyd Williams, playing on the wing, chipped infield and Gareth Davies calmly gathered the bouncing ball to score under the posts to stun England.
Biggar's conversion tied the scores at 25-25 with eight minutes left and suddenly England looked shell shocked.
At this point, Wales had lost three backs - in a four-minute spell - to add to its extensive injury list to leave the back division with two scrumhalves, two fly halves and three players out of position.
Biggar nosed Wales in front with his seventh penalty, but England had a chance at a draw when they earned a penalty with two minutes left. Robshaw electedto go for a lineout rather than give Farrell - who had been six from six from the kicking tee - a shot at goal from the right touchline.
The decision backfired, as Wales' pack snuffed out the danger with a big shove. The final whistle was met by disbelief from the majority at Twickenham.
"I don't think I've shown as much emotion at the final whistle as I have tonight," Wales coach Warren Gatland said. "I can't ask for any more. I think they (Wales' players) wanted it more in the end."
"I thought they would have gone for goal and taken the draw. It was a brave call to me. We did a good job to stop that driving maul. Personally, I would have taken the three points."
Sam Warburton was also a relieved man at the final whistle, but never had any doubt his team could defend the vital lineout to deny England the crucial try they needed to win the game.
"We were put in a similar situation against South Africa last year. There is nothing technical about it. It's just the will to win. You look at the other players in the eye, it's all about heart," he said.
The only downside to the victory is the number of injuries sustained. Liam Williams, Scott Williams, Hallam Amos will all need assessing ahead of the next game against Fiji.
"England were in a similar situation in the Six Nations. People were saying that we didn't have the strength in depth to come to England and win but the quality of the guys who came off the bench is incredible. I do believe in the strength in depth of this squad and I'm really proud of the boys tonight," concluded Gatland.
