Williams has been rewarded for his hat-trick against Namibia, with the Scarlets centre ousting Jonathan Davies.
And Roberts believes that the 20-year-old can rise to the challenge of facing Fiji in the Waikato Stadium.
"You can't take anything away from what Scott did on his first start," Roberts said. "He played a fantastic game against Namibia.
"Scott has a lot of maturity with his passing and his skill. He's quite quiet in his approach, but he goes about his work very well. Hopefully, he is going to thrive.
"I can't think of anywhere better really for someone 20 years of age to be playing, at a World Cup in a pool match against Fiji that could take us into the quarter-finals."
Wales, who can only be denied a last-eight place if they suffer a 62-point defeat against Fiji, are likely to meet Ireland at the quarter-final stage next Saturday.
Ireland's stirring Pool C success against Australia a fortnight ago blew open the draw's top half, and it was a performance that left an impression on Roberts.
"I thought Ireland played perfect rugby in the conditions that day," he said.
"Their kick-and-chase game was spot on to beat a southern hemisphere team. When you are playing Australia and it's hot and sunny, the Wallabies are freakishly dangerous.
"Ireland are a very dangerous team, as we are well aware. I am sure if it does come to the quarter-finals it would be a hell of a game.
"We have to go flat out against Fiji. We want to beat Fiji well to take that momentum into the quarter-final."
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