Capuano (4-6) scattered six hits and a walk, and struck out five while going 6 1/3 innings that stretched his scoreless innings streak to 13.
Brandon League, Ronald Belisario and Paco Hernandez teamed up for 1 2/3 shutout relief innings and Kenley Jansen struck out two in the ninth for his 16th save as the streaking Dodgers set a club record for most consecutive road victories.
National League West-leading Los Angeles reeled off a third straight triumph against Chicago and a 30th victory in 37 games overall.
The loss was hung on Chicago's Jeff Samardzija (6-10), who gave up three runs on seven hits and five walks in six innings.
Susan Sarandon 'very excited' about daughter's pregnancy
Interpol investigating stolen passports on missing flight