Cubs pitcher Ted Lilly (6-4) and the Dodgers starter Chad Billingsley (6-3) each opened with six scoreless innings.
Matt Kemp hit his fifth home run with two outs in the top of the seventh. The Cubs bounced back in the bottom half and ended Los Angeles' four-game winning streak.
Hill led off the Cubs' seventh with his second homer, just over the wall in right field. With one out, pinch-hitter Jake Fox, Alfonso Soriano and Bobby Scales each singled to load the bases for Fukudome, who hit a high flyball to center field.
Kevin Gregg pitched the ninth, and held on for his eighth save in nine chances. Andre Ethier singled with two outs and Kemp reached on Scales' error at third base, but Gregg got pinch-hitter Mark Loretta to ground into a force play.
Lilly, who had lost his previous two starts, gave up four hits in seven innings, striking out five and walking three.
Billingsley lost his seconds straight start. He allowed both runs and eight hits in seven innings, striking out seven.
Playing with several substitutes in the starting lineup, the Cubs continued to waste scoring opportunities against the NL West-leading Dodgers. After blowing several late scoring chances in their 2-1 loss to the Dodgers on Thursday.
Derrek Lee led off the second with a walk and Micah Hoffpauir doubled him to third. But Mike Fontenot lined out to second, Hill struck out and Andres Blanco popped up.
