With San Francisco trailing Atlanta by one-half game for home-field advantage throughout the National League playoffs, the Giants had a chance to move ahead of the Braves with a doubleheader sweep.
Robin Ventura had a double to center giving Los Angeles a 1-0 lead.
Jackson (2-1) gave up a double in the third inning and a single in the sixth but issued eight walks. The righthander, who was making his third major league start, also struck out seven.
Notable deaths of 2014 [PHOTOS]