Hernandez hit his sixth home run of the year in the ninth inning to cap the scoring.
Vasquez took the loss for San Diego after giving up six hits and three runs.
The Padres loaded the bases with one out in the bottom of the fifth, but Fernando Tatis Jr. grounded into an inning-ending double play on Ohtani's final pitch.
Four Los Angeles relievers combined to finish the five-hitter, preserving the shutout as San Diego went scoreless over the final 15 innings of the series.
Padres center fielder Jackson Merrill left the game in the fifth inning after crashing into the outfield wall while attempting to catch Ohtani's home run.
The victory gave Los Angeles two wins in the three-game series and extended their lead over San Diego in the National League West standings.
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Both teams have a scheduled day off Thursday before the Dodgers open a series in Milwaukee on Friday and the Padres host the Athletics.
NL West Standings Entering Wednesday
- Los Angeles Dodgers: 30-19 (—)
- San Diego Padres: 29-19 (0.5 GB)
- Arizona Diamondbacks: 24-23 (5.0 GB)
- San Francisco Giants: 20-29 (10.0 GB)
- Colorado Rockies: 19-30 (11.0 GB)
