An error by shortstop Hanley Ramirez paved the way for a four-run third inning against Maholm.
"You're going to have days like this. I've had worse," said Maholm, the backup to Josh Beckett as the fifth starter. "For me, what's important is to be healthy and get my mechanics where they need to be and go from there."
In addition to the solo homer by Frazier and the three-run shot by Heisey, Maholm allowed a double to Ramon Santiago, who later had a second hit.
The Dodgers scored in the fourth inning on singles by Juan Uribe, Andre Ethier and Scott Van Slyke before Justin Turner's sacrifice fly. Ramirez homered off Lee Hyde in the fifth inning, clearing the left-field grass berm.
Cincinnati added a run in the eighth off Dodgers Rule 5 acquisition Seth Rosin. Dodgers non-roster pitcher Red Patterson preceded Rosin with 3 1/3 scoreless innings on one hit.
Up next: The Dodgers make their first trip to new Cubs Park on Friday to face the North Siders at 1:05 p.m. PT. The game can be seen live on MLB.TV.
Beckett said he plans to make the start against the Cubs despite a sprained right thumb. The right-hander was hit by an opening clubhouse door about 10 days ago. Up to that point, Beckett was having a healthy recovery from last year's thoracic outlet syndrome surgery.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.