Fife (4-3) scattered seven hits and two walks over 5 1/3 innings, striking out five en route to the victory.
Chris Withrow and J.P. Howell teamed up for 2 2/3 scoreless relief innings and Kenley Jansen struck out the side in the ninth for his 17th save as the National League West-leading Dodgers reeled off their 31st win in 38 games.
A.J. Ellis provided the game's only run with a RBI single in the second inning.
Chicago's Carlos Villanueva (2-8) was saddled with the hard-luck loss, yielding just the one run on two hits over six innings. He walked three and struck out five.