The Dodgers now need just one win to reach the World Series.
"It's huge," Kershaw told reporters. "I think it wasn't as easy as last year maybe to get to this point. We realize we have some work to do to finish it off and get back. If you would have told us in spring training we had a chance to go the World Series with one game to go, we would have definitely taken that."
"It doesn't really matter how you get here, but I am thankful we are here now."
Lorenzo Cain doubled in the first run of the game, putting the Brewers up 1-0 with an RBI double in the top of the third inning at Dodger Stadium.
Kershaw kept the Brewers bats quiet for the remainder of his stay on the mound, allowing Dodgers catcher Austin Barnes to tie the game with an RBI single in the bottom of the fifth frame. Max Muncy gave the Dodgers a 2-1 lead with another RBI single in the bottom of the sixth inning.
Yasiel Puig put the Dodgers up 3-1 with another RBI single in the same frame. The Dodgers added on to their lead in the seventh inning. Justin Turner raked an RBI single for a 4-1 advantage before Brian Dozier plated Cody Bellinger with an RBI ground out to give the Dodgers a 5-1 lead after seven innings.
Kershaw had nine strikeouts and two walks in addition to allowing one run. The Brewers attempted to mount a comeback in the top of the ninth inning, but could only plate one run off of a Curtis Granderson double. Kenley Jansen ended the game by striking out Mike Moustakas, clinching the Dodgers victory.
"He's [Kershaw] is our guy," Turner told MLB Network. "He's our horse. He is the guy we always want to have the ball. We know when he is out there, we have a really good chance to win the ball game. He was absolutely outstanding today."
Game 6 of the 2018 NLCS is set for 8:39 p.m. on Friday at Miller Park in Milwaukee.
"There were so many good things that we did today and it helped us win a baseball game," Dodgers manager Dave Roberts said. "Clayton was outstanding today. He mixed his pitches really well ... He settled in and gave us that length that we needed. We kinda fed off of that."
Moments from the MLB post-season