Woodruff's third inning shot tied the game on Friday at Miller Park in Milwaukee. The Brewers took a 2-1 lead later in the inning and eventually pushed the advantage to five runs. Los Angeles responded by posting four unanswered runs but could not complete the comeback.
"I was just trying to get them fired up," Woodruff told reporters. "You know, obviously in the postseason, a lot of things can happen. I thought that that was a big moment to kind of get the guys going."
Manny Machado hit a solo home run in the top of the second inning to give Los Angeles an early 1-0 lead.
Woodruff got the Dodgers out in order in the top of the third inning, before stepping in to leadoff the order in the bottom of the frame. Kershaw tossed a 90.7-mph fastball for a ball before getting two called strikes on the pitcher. Woodruff worked the count to 2-2 before Kershaw's final offering of the exchange.
Woodruff smacked the 92-mph fastball to center field for a 407-foot bomb. The long ball had an exit velocity of 101-mph, according to Statcast.
"That was the next level up," Brewers manager Craig Counsell said. "I've never seen Brandon like that. To make the first run your team scores in the NLCS a homer off Clayton Kershaw, that's how you should run around the bases. That's exactly how you should run around the bases."
"The thing is, it just fired everybody up. The crowd went crazy. And our dugout, it certainly changed the energy in our dugout from what you think is going to be kind of a grinded-out game against Clayton. When that happens, it gives everybody life."
Lorenzo Cain came around to score on a sacrifice fly by Hernan Perez, giving the Brewers a 2-1 advantage in the third frame.
Domingo Santana plated Chris Taylor and Manny Pina with an RBI single in the bottom of the next inning. Ryan Bruan brought in Santana on a single in the same inning to give the Brewers a 5-1 advantage.
Jesus Aguilar hit a solo home run in the bottom of the seventh inning to give Milwaukee its biggest lead of the bout.
Then the Dodgers began their comeback. Machado knocked in Joc Pederson and Taylor on an RBI single in the top of the eighth inning. Matt Kemp made the score 6-4 with another RBI single in the same frame.
Taylor got the dodgers even closer with an RBI triple in the top of the ninth inning, but Brewers reliever Corey Knebel struck out Justin Turner to end the game.
The Brewers host the Dodgers in Game 2 of the 2018 NLCS at 4:09 p.m. on Saturday in Milwaukee.