Navarro followed with a game-winning single for the Dodgers, who clinched their three-game series with San Diego.
Four Dodgers pitchers combined for a complete-game one-hitter, led by starter Rubby De La Rose, who yielded only one hit over six no-run frames, walking four and striking out eight.
Matt Guerrier and Mike MacDougal each tossed a scoreless inning and Blake Hawksworth (2-2) hurled a 1-2-3 ninth to earn the victory.
Cameron Maybin got the Padres' only hit.
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