The Israel-Premier Tech rider out-paced stage one winner Paul Magnier and Edoardo Zambanini in a sprint finish after his team managed to neutralise several attempts at a breakaway.
"It was a really hard day, really demanding," said Williams after a rainswept 166 kilometres from Sheffield to Barnsley.
"It was a real privilege to be a part of - the team were unbelievable, exceptional. The way they rode that and controlled it was amazing.
"I'm really proud to bring it across the line. I did the last kilometre, but they did the four hours before it."
Victory extends Williams' lead in the general classification to 16 seconds from Britain's Oscar Onley with Mark Donovan, Joe Blackmore and Tom Donnenwirth all 41 seconds off the lead.
The fourth of six stages runs 138.5 kilometres from Derby to Newark on Friday.
