Cody Bellinger followed with a two-run homer that gave the Dodgers a 2-1 lead.
Kenley Jansen tossed 1 1/3 scoreless innings before yielding to Kershaw in the ninth.
Yelich looked like he would get to the Dodgers again in the fifth with Lorenzo Cain on second with two outs. The Dodgers return for a second straight year, creating a rematch of the 1916 Fall Classic, won in five games by Boston, who was led by a 21-year-old pitcher named Babe Ruth. The victor, of course, will move on to face the Boston Red Sox in the 2018 World Series.
Clayton Kershaw ended this one by pitching a ideal ninth inning, beginning the official Dodgers celebration, amid silence from most of the sellout crowd of 44,097.
The Dodgers have talked about having unfinished business after losing Game 7 of the World Series previous year to the Houston Astros.
"Chacin go six. Hader go three".
Manny Machado - serenaded by boos each time up - bunted for a single against Chacin in the second and grabbed his crotch to taunt the fans.
Bellinger raised his right arm and pointing to his biceps as he rounded third after his homer.
Goliath match-up of big-money Dodgers versus small-market Brewers provided all sorts of drama, but in the end, the Dodgers' strong pitching, some sterling defense, and Puig's power proved too much. A late surge led by Yelich lifted Milwaukee from 5 1/2 games out of the NL Central lead on August 28 to one win short of the franchise's second World Series appearance.
With the series now tied for the Brewers, fans are anxiously awaiting the outcome of Saturday night's game. It was Puig's first home run of the championship series.
They'll have to dethrone the Dodgers.