Williams scored twice and Rod Brind'Amour had two assists to help Carolina beat the Atlanta Thrashers 4-1 on Saturday night.
"We have to play like every game is the most important," Williams said. "We were active all night. We were jumping."
Mike Commodore and Ray Whitney also scored for Carolina, which has won two straight and six of nine to move past Montreal into seventh place in the Eastern Conference. With 71 points, the Hurricanes are just one point behind struggling Atlanta for second place in the Southeast Division.
"I thought our defence played an excellent game," said Carolina coach Peter Laviolette, whose team beat Edmonton in seven games to win the Stanley Cup last year. "Our forwards did a good job of coming back to help the defence."
Atlanta has lost five straight at home, one in overtime and another in a shootout. The Thrashers have earned just four points out of a potential 14 in the last seven games at Philips Arena.
Since winning their first game after the all-star break, the Thrashers have dropped nine of 13 overall.
"I have to admit we have some guys who are really struggling with the pressure," coach Bob Hartley said. "They're tight, they're not comfortable, and we'll have to find a solution or medication to get them to play the game. You have to be ready to do the little details, blocking shots, chipping it deep, forechecking. But unfortunately sometimes right now, some guys are having a hard time with those details."
After the game, Atlanta acquired veteran defenceman Alexei Zhitnik from Philadelphia for six-foot-five, 220-pound defenceman Braydon Coburn.
Zhitnik, an all-star in 1999 and 2002, has five goals and 18 assists in 60 games with the Flyers and New York Islanders this season.
Coburn, the eighth overall pick in the 2003 draft, has spent most of the last two seasons with the Thrashers' AHL affiliate in Chicago.
Williams made it 1-0 with his 30th goal 15:07 into the first, snapping the puck over the outstretched right pad of goalie Kari Lehtonen.
"I was stuck on 29 for a while, but we don't need to look at personal stats," Williams said. "As a team, we're in seventh place. It's going to be a grind down the stretch."
With 6:35 left in the third, Williams' breakaway goal made it 3-1.
The Thrashers cut the lead to 2-1 when Garnet Exelby scored his first career short-handed goal with a slap shot from the blue-line that beat John Grahame stick side.
"It was very important to get out to a two-goal lead," Grahame said. "It's nice to have a cushion when you play a skilled team like Atlanta."
Commodore made it 2-0 with his fifth goal after Brind'Amour's pass to Whitney ricocheted to the right circle.
Brind'Amour got his second assist on Whitney's empty-net goal with eight seconds remaining.
Hartley refuses to place too much blame on Lehtonen, who has lost four straight starts and is 2-7-1 since winning consecutive games against the New York Rangers and Islanders last month.
Perhaps the acquisition of Zhitnik will give Lehtonen more support.
"We have to find solutions," Hartley said. "It's as simple as this. We're working with players, but I don't think that the problem is the game. It's the human side. It's a game, and there's going to be a winner and loser, but if you prepare yourself accordingly, chances are you're going to come out on the right side. Over the past weeks, we've been having a hard time with this."
Notes: Exelby has two goals this season. ... The Thrashers fell to 4-10-2 against Carolina at Philips Arena. ... Whitney's 45th assist gave him a point in 17 of 21 games. ... Hurricanes left wing Cory Stillman, who returned after missing the previous seven games with an injured knee, played 12:06 in 17 shifts. ... Carolina is 14-7-2 against the Southeast Division, while the Thrashers are 13-5-6.