Williams put the Hurricanes up 1-0 at 4:34 of the second period when he chipped in a rebound off a shot from Dougie Hamilton. It was his 11th goal of the season.
"We played a really good game on the road," Hurricanes goalie Petr Mrazek said. "We battled hard and it's too bad we didn't get any points from it."
The Hurricanes outshot the Lightning 12-3 in the first period and held a 24-17 shot advantage with 11 minutes left in the third. Mrazek made 27 saves; Andrei Vasilevskiy made 26.
"We just didn't have our legs," Tampa Bay coach Jon Cooper said. "It seemed like we were in quicksand. It was both teams probably. They got a little life there at the end of the first. It took us a bit to get going, but when we did it was good."
The Hurricanes were called for six penalties.
"We knew coming in we couldn't take penalties and we did," Carolina coach Rod Brind'Amour said. "It's too bad. It was a good game. Both teams played pretty hard, I thought, and they got the better of us."