Kiké Hernández hit a two-run shot to make it 4-0 in the sixth inning and waved to the Citi Field crowd he quieted. Los Angeles rebounded from a loss at home and grabbed a 2-1 lead in the best-of-seven series by pitching its fourth shutout in the past five playoff games.
Ohtani connected in the eighth, a 410-foot drive that soared into the second deck in right field and barely stayed fair above the foul pole.
Max Muncy went deep in the ninth for his 13th career postseason homer, tying Corey Seager and Justin Turner for the franchise record. Muncy also connected in Game 2.
A fired-up Walker Buehler struck out Francisco Lindor to leave the bases loaded, and the Dodgers got five stingy innings from their hard-throwing bullpen. Buehler combined with four relievers on a four-hitter.
Game 4 is Thursday night in Queens, with $325 million rookie Yoshinobu Yamamoto scheduled to start for Los Angeles against veteran left-hander Jose Quintana.
Los Angeles now stands just two wins away from returning to the World Series for the fourth time in less than a decade under manager Dave Roberts.
In the American League Championship Series, the New York Yankees now hold a 2-0 lead over the Cleveland Guardians. They play Game 3 Thursday afternoon.