"We didn't let the game get away from us," Williams, whose team has won five of seven, told the Kings' official website. "We killed a penalty when we needed to and we scored a power-play goal when we needed to. We won one in overtime. Big division game.
"We needed a come-from-behind win, and we got it. It took us (62 1-2) minutes, but eventually we got it done."
Los Angeles will try to get it done Saturday without Jeff Carter, who is tied with Williams for the team lead with five goals. Carter is going on injured reserve due to a lower-body injury.
The Predators (6-5-2) kicked off a franchise-record 17-day, seven-game road trip in disappointing fashion with a 5-4 shootout loss to Phoenix on Thursday. David Legwand scored and recorded a season-high three points, but Nashville let up after building a 3-0 lead in the first period.
"We just shot ourselves in the foot. It's just frustrating," left wing Eric Nystrom, who also scored, told the team's official website. "Everything was preventable. Those can't happen. That's tough. We should have had two points in that game, 100 percent.
"We just let off the gas pedal, and a couple of broken plays end up in our net, and that's got to be the only time that happens this year."
The Predators outshot the Coyotes 40-25 before missing all five shootout attempts. Carter Hutton, making his third consecutive start in place of the injured Pekka Rinne, dropped to 0-1-1 with a 4.79 goals-against average in his last two games.
Nashville has allowed 14 goals during a 1-2-1 stretch.
"We made too many mistakes," coach Barry Trotz said. "That's not smart hockey."
The Predators will surely need a better effort in goal if they hope to beat the Kings, who are 9-3-1 in the last 13 meetings. Los Angeles pulled out a 2-1 shootout victory in Nashville on Oct. 17 behind a rare goal from Slava Voynov and Jonathan Quick's 34 saves.
Beating the Predators hasn't been easy for Quick, who entered that game with a 1-5-2 record and 2.85 GAA in the series.
Quick has won three consecutive starts and is 5-1-0 with a 2.26 GAA over the last two weeks. He is also 5-1-0 in his last six home starts.
Leading the team with 13 points, Kopitar has gone without one in his last four matchups against the Predators.
The Predators, near the bottom of the NHL with 2.08 goals per game, are 3 for their last 22 on the power play. They may be able to break out against a Kings team that has surrendered seven power-play goals in 23 chances over a five-game stretch.