Cruz delivered a two-run single in the fourth inning to hand the Dodgers a 4-0 lead and made it 5-0 an inning later with another run-producing hit.
Billingsley (9-9) baffled the Pirates on five hits, issued only one walk and struck out five in notching his fifth consecutive win.
The Dodgers -- who came into the game tied with the San Francisco Giants for first place in the National League West -- notched their fifth win in six games.
Pirates starter Kevin Correia (9-7) was roughed up for six runs (five earned) on seven hits over six innings.
Pittsburgh lost for the eighth straight time against Los Angeles.
2014: The Year in Music [PHOTOS]