Norm Charlton, the fourth Cincinnati pitcher, got the last three outs.
Parent singled with one out in the 12th off Tim Birtsas (2-1), the fourth Cincinnati pitcher.
John Franco (3-4), the sixth Cincinnati pitcher, pitched one perfect inning for the victory.
Supported by a 16-hit assault on four Cincinnati pitchers, Dennis Martinez (11-1) won his 10th straight decision.
Tim Birtsas (1-0), the sixth Cincinnati pitcher, allowed one hit and one run over the last three innings.
John Franco, the fourth Cincinnati pitcher, closed the game for his 13th save.
Rijo also singled twice, scored once and stole a base, the first time this season a Cincinnati pitcher has attempted to steal.
Pat Perry (2-2), the sixth Cincinnati pitcher, pitched three hitless innings for the victory.
Bill Phillips, with a 14-18 record and a 4.64 ERA, was the only other Cincinnati pitcher to have ten or more victories.
John Franco, the fourth Cincinnati pitcher, worked a perfect ninth for his 31st save.