Napoli's solo shot off Justin Miller gave the Angels a 6-3 lead, which they needed as the Dodgers scored twice in the bottom of the frame to add suspense.
But Brian Fuentes tossed a scoreless ninth inning to notch his 10th save and lift the Angels to their first-ever sweep at Dodgers Stadium in the annual crosstown inter-league series between the teams.
Jered Weaver (6-3) held the Dodgers to three runs on five hits over six innings, walking only one and fanning seven.
Torii Hunter knocked a solo homer and Hideki Matsui was 3-for-4 with a pair of RBI in the Angels' win.
Dodgers starter Carlos Monasterios (3-1) was saddled with his first loss of the year, lasting only 2 2/3 innings. He surrendered four runs on seven hits.