The win pushes Los Angeles to within two games of advancing to the World Series for the first time since 1988.
Turner came to bat in the 9th with Yasiel Puig and Chris Taylor on base and two outs, with the score at 1-1. In a post-game interview, he said it was the first walk-off homer he hit in his career.
"We've been doing it all year long," Turner said. "We're never out of a game. As long as we have outs left, we're going to keep fighting."
The homer came 29 years to the day on the anniversary of Kirk Gibson's still-celebrated walk-off home run in Game 1 of the 1988 World Series, giving the Dodgers the win over the Oakland Athletics.
"It's very cool, and J.T., we were talking about it in there after the game," Dodgers manager Dave Roberts said. "Twenty-nine years to the day. It was special. Our guys feel it."
Turner's home run was the Dodgers' first walk-off homer in the postseason since Gibson's famous shot.
Completing the poetry of the moment, a fan in a Chase Utley jersey in the center-field bleachers reached over a railing to catch the ball in his glove.
Turner drove in every run for Los Angeles, getting an early RBI single before sending the long shot to center off John Lackey in the ninth.
The 4-1 win at Dodger Stadium brings the seven-game National League Championship Series to 2-0 in LA's favor.
Rich Hill started on the mound for the Dodgers - a decade after he made his postseason debut for the Cubs. Kenley Jansen was brought in for the save.
Left-hander Jon Lester started for Chicago, with John Lackey brought in to attempt a save with no rest after relieving in Game 1.
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The Dodgers won the first NLCS game 5-2 at home.
Game 3 is Tuesday night at Wrigley Field. Yu Darvish is expected to start for the Dodgers, with Kyle Hendricks on the mound for the Cubs.
The Associated Press contributed to this report.