After losing at Twickenham an away victory over the Irish would leave Wales in a healthy position to attack their final two home games against Italy and France.
Unbeaten England have to go to Edinburgh and Paris and Williams knows that one slip-up from Andy Robinson's men could open the door for Wales.
But to remain on England's coat-tails, Wales must get that win in Dublin, a city that has not been kind to the red dragon in recent years.
Wales have lost on each of their last three visits to the Emerald Isle - conceding 125 points in the process - but Williams insists: "We have not written ourselves off in the hunt for the championship.
"Ireland is a massive game for both sides, it will probably decide how we finish off in the table.
"There are not many tougher places than Ireland and from the way they finished off against France they will be full of confidence.
"It is good to have three games at home - so if we can win away and then come back for our last two games at the Millennium Stadium it would be great for us.
"We got stronger as the tournament went on last year and we would like to do the same this year.'