The victory came in the opener of a three-game series at Petco Park.
Cameron doubled, tripled, belted a three-run homer and came to the plate in the bottom of the seventh inning needing a single to complete the cycle.
The outfielder ended up walking, which elicited jeers in the direction of Dodgers pitcher Odalis Perez.
"I was trying to go up there and make history. Unfortunately Odalis didn't want to throw any strikes," said Cameron.
Vinny Castilla drove in three runs and Eric Young hit the first pinch-hit homer of his career for San Diego, which snapped a two-game losing streak.
Chan Ho Park (4-3) surrendered one run on three hits with three walks and five strikeouts in six frames to pick up the victory.