NEW YORK – To extend their season another day, the New York Yankees needed that big, momentum-changing hit that eluded them through the first three games of the World Series. They were on the brink of elimination in Game 4 at Yankee Stadium on Tuesday night.

Anthony Volpe hit a go-ahead grand slam in the fourth inning, Austin Wells added a solo shot two innings later and Gleyber Torres put the finishing touches on an 11-4 victory over the Los Angeles Dodgers with a three-run home run. the eighth inning when the Yankees avoided elimination for at least one night.

Volpe’s breakthrough came on a first-pitch slider by Daniel Hudson, the second reliever the Dodgers used for their scheduled bullpen day, with two outs and the Dodgers leading 2-1. The grand slam, which landed a few rows past the wall in left field, galvanized a sellout crowd that was on edge after Freddie Freeman’s two-run home run in the first inning.

It was Volpe’s first career grand slam and the first by a Yankee since Tino Martinez in Game 1 of the 1998 World Series against the San Diego Padres. At 23 years and 184 days old, Volpe became the youngest Yankee to hit a grand slam in the World Series since Mickey Mantle in 1953.

It wasn’t a promising start for the Yankees. Freeman’s home run — a laser beam over the short right-field porch of Yankees starter Luis Gil that extended his World Series home run streak to a record six games — immediately deflated the crowd. It put the Yankees, who had not led since Freeman’s walk-off grand slam in Game 1, in an early hole for the third straight game. But the Dodgers’ reliever carousel couldn’t stop the Yankees.

Five Yankees relievers, meanwhile, were not charged with a run over the final five innings of the game. The quintet of Tim Hill, Clay Holmes, Mark Leiter Jr., Luke Weaver and Tim Mayza held the Dodgers without a hit after the fifth inning. It was the formula the Yankees were looking for in this series. It saved their season on Tuesday.