Fife (1-0), making his second start of the season and seventh of his career, allowed one run on five hits. The 25-year-old right-hander walked two and struck out five.
Peter Moylan, Paco Rodriguez and Kenley Jansen combined for 2 2/3 scoreless relief frames and Brandon League collected his 12th save as Los Angeles took the opener of a three-game set.
Adrian Gonzalez and Scott Van Slyke each knocked a solo homer to provide the Dodgers' offense.
Padres starter Eric Stults (4-5) absorbed the loss, surrendering two runs on six hits over seven frames.
Chase Headley drove in San Diego's only run.