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.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
18-year-old elf alleges mall Santa pinched her buttocks on the job