Capuano (1-2) pitched well in his second start since coming off the disabled list, baffling the Marlins, who managed just one run off him. The left-hander yielded five hits and one walk while striking out seven.
Scott Van Slyke socked a solo homer and added an RBI single for the Dodgers, who posted a second consecutive win over Miami after snapping an eight-game losing streak Saturday.
Carl Crawford went 2-for-4 with an RBI in the victory.
The loss was hung on the Marlins' Tom Koehler (0-1), who made his second major-league start. He allowed two runs on seven hits while lasting five frames.
Justin Ruggiano went 2-for-4 with a solo homer and Adeiny Hechavarria drove in a pair of runs for Miami.