And an overjoyed Williams, winning his 78th cap for Wales, revealed the magnificent win at England's HQ was a sweet feeling.
Williams said: "It's one of the best wins of my career without doubt. We're the first Welsh team to win here for 20 years and it's a great achievement. The players are over the moon.
"We've come up here before in hope but this time we genuinely believed we belonged here. The results of the Ospreys and the Blues in Europe have definitely helped us.
"After Mike scored we felt we were in the ascendancy and confident we could do it. We maybe should have been more ruthless and gone for a drop goal but that would have been greedy. The tight five really fronted up at the end of the first half and start of the second which swayed the match for us and kept us within two scores.
"We knew we had a strong bench and we were building momentum and it was hard for them to stop us. They may have relaxed but we were never comfortable. It was a nice feeling knowing we had the game by the scruff of its neck with minutes remaining and we managed to run the clock out.
"When a new coach comes in, everyone works harder and you get an instant reaction but we can't get carried away. We have to keep working hard and built in these championships because if we don't win against Scotland next weekend, this result will not matter."