Kyle Tucker drove in two runs with a single, and a third run scored before Hughes settled in, retiring 15 straight Dodgers through the sixth inning.
However, the early lead evaporated by the third inning against Dodgers starter Roki Sasaki, who surrendered two solo home runs in the second inning, including one to Kyle Karros.
The broadcast call highlighted the significance, as the batter's father, Eric Karros, was calling the game for SportsNet LA.
"A bullet of a home run at Dodger Stadium. You've heard that a couple hundred times," said broadcaster Joe Davis.
"This time it's Kyle."
Sasaki completed six innings, allowing three runs while striking out five before the bullpen took over.
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The Dodgers will take Thursday off before opening a home series against the Arizona Diamondbacks on Friday night, with Shohei Ohtani scheduled to start on the mound.