Justin Williams scored twice for the Kings, Drew Doughty had one goal and Willie Mitchell added two assists. Jonathan Quick made 22 saves to out-duel Nashville's Pekka Rinne, who was pulled in the third period after giving up five goals on 24 shots.
"For us to make the playoffs, it's pretty simple," said Los Angeles head coach Darryl Sutter. "Your best players have to be your best players. It's not that hard to figure out. It's not about singling anybody out, or anything like that."
Patric Hornqvist scored his second goal with 5:18 left to get the Predators within 5-4, but they couldn't find the equalizer. The other goals came from Martin Erat and Sergei Kostitsyn.
The Kings have won two of three meetings between the teams this season with a fourth game scheduled for March 17 in Los Angeles.
They took a 4-3 lead on Greene's slap shot from high on the right side, which beat Rinne 75 seconds into the third period after making it through traffic in front. Lewis scored just 1:45 later after Anze Kopitar's failed wrap-around ended up in front for an easy stuff.
Anders Lindback stopped all four shots he faced after Rinne was taken out and Hornqvist gave the Predators hope with a weird goal that was reviewed.
Kings defenseman Willie Mitchell fell down in the slot, leaving Hornqvist all alone against Quick, who poke-checked the puck into the forward's right skate. It deflected into the air and past the goaltender to get Nashville within 5-4 but all further attempts failed and Quick finished with nine saves in the third period.
Williams scored two goals in the first period, including one Rinne knocked in himself while skating backwards after the Kings forward flipped the puck on net from the right corner. Hornqvist scored his first goal later, but Williams replied with a tally 12 seconds after that.
"We have to play more consistent. We have to play a 60-minute game," Hornqvist said. "We turned the puck over way too many times tonight, but you have to give the Kings credit, too. They stepped up."
Erat and Kostitsyn scored for Nashville in the second period and Doughty had a goal for the Kings.
The Predators started a three-game homestand that includes games against the Avalanche on Thursday and Red Wings on Saturday...The Kings, who have won three in a row, opened a four-game road trip that will also take them to Columbus, Detroit and Chicago...Nashville went 0-for-3 on the power play and LA was 0-for-1.