Muncy’s homer to left-center field on a 3-2 pitch negated a heroic relief effort by Boston’s Nathan Eovaldi, who threw more than 100 pitches in six innings.
Game 4 is Saturday night at Dodger Stadium.
The game, which stretched past seven hours, also was the longest World Series game in terms of time, breaking the 5-hour, 41-minute marathon between the Chicago White Sox and Houston Astros in Game 3 of the 2005 World Series, which went 14 innings.
It was the longest postseason game between the two teams since Boston won 2-1 in 14 innings during the 1916 World Series. The winning pitcher that day was Babe Ruth, who pitched a complete game.
Muncy nearly ended the game in the 15th inning when his drive down the right-field line was barely foul. He scored on a two-out throwing error in the bottom of the 13th to tie the game at 2-2. Muncy led off with a walk and went to second when Eduardo Nunez tumbled into the third-base stands to catch Cody Bellinger’s pop foul.
With two outs, Yasiel Puig grounded to Ian Kinsler, who threw wildly to first to allow Muncy to score the tying run. Puig’s grounder was ruled a hit and an error.
Boston had gone ahead in the top half of the 13th to take a 2-1 lead.
Brock Holt led off the inning with a walk off Scott Alexander and then stole second. Eduardo Nunez then chopped a ground ball between first base and the pitching mound, but Alexander’s bad throw got past Muncy, allowing the go-ahead run to score.
Los Angeles’ Joc Pederson hit a two-out, solo home run off Boston starter Rick Porcello in the bottom of the third inning to give the Dodgers a 1-0 lead. The Red Sox tied the game in the top of the eighth when Jackie Bradley Jr. homered off Dodgers reliever Kenley Jansen.
The Red Sox put runners at first and third with one out in the 10th, but Cody Bellinger threw out Ian Kinsler at the plate after catching Nunez’s fly ball in center field drive to complete an inning-ending double play.