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Ireland, chasing 328 for victory, won with five balls to spare as they finished on 329 for seven.
It seemed as if England, who made 327 for eight, were cruising to victory when they reduced non-Test playing Ireland to 111 for five.
But in a brilliant burst of power-hitting O'Brien got to three figures in just 50 balls at the Chinnaswamy Stadium.
That meant he'd obliterated former Australia opener Matthew Hayden's previous fastest World Cup century record off 66 balls against South Africa at St Kitts in 2007.
O'Brien's whirlwind innings of 113 off 63 balls, including six sixes and 13 fours, ended when he was run out going for a second run by Tim Bresnan's throw to wicketkeeper Matt Prior.
Ireland's target was down to three off the last over but they won with five balls to spare when John Mooney struck a four off James Anderson.
It was the highest successful run chase in World Cup history.
"It's pretty amazing," said Ireland batsman Alex Cusack, who made 47 in a decisive sixth-wicket partnership of 162 with O'Brien.
"Words can't describe how I feel at the moment, just on top of the world.
"We decided if the ball was there that we'd have a go at it. I was just trying to knock it around for Kev. He's got the power. That was my job and he was playing the big shots."
Fastest Cricket World Cup Centuries:
1. Kevin O'Brien (Ireland) v England 2011 50 balls
2. Matthew Hayden (Australia) v South Africa 2007 66 balls
3. John Davison (Canada) v West Indies 2003 67 balls
4. Kapil Dev (India) v Zimbabwe 1983 72 balls
5. Adam Gilchrist (Australia) v Sri Lanka 2007 72 balls
