The last side to storm England's stronghold in a Test match were New Zealand during the 1999 World Cup but O'Sullivan believes that proud record will only provide his side with more motivation to cause a shock upset.
"We have to go into Saturday's match with a view that we can win every game," he said.
"This is a match we can win and the prospect of being the first team to succeed at Twickenham in four and a half years is a great carrot.
"We've had a couple of good results against Australia and France in recent years but to turn the world champions over would be the cherry on the cake - that's what every team wants to do.
"It's great for the Six Nations to have the World Cup winners in the tournament. As the World Cup had always been won by the Southern Hemisphere sides in the past, it meant we could only play the winners when we - or they - were on tour.
"Now we'll get a crack at them every season and that's what every team wants."
Ireland enter the repeat of last year's Grand Slam decider on the back of a convincing 36-15 victory over Wales, allowing O'Sullivan to name a virtually identical team to the side which triumphed at Lansdowne Road 10 days ago.
The only change comes in the forwards with Leinster second row Malcolm O'Kelly replacing the injured Donncha O'Callaghan who strained the medial ligament in his right knee against Wales.
"I was happy with the way we played against Wales so the team selection was very simple and there wasn't much to talk about," said O'Sullivan.
"There were no areas of debates. I am happy with the way Gordon and Brian played as a pair so I'll stick with them."