Dontrelle Willis, who is fighting for the final spot in the Reds' bullpen, allowed five runs on three hits and three walks while recording only one out.
After missing his last start with a hip flexor, Stauffer earned the victory by limiting Cincinnati to two runs on six hits and a walk in six innings pitched. Stauffer struck out four.
Venable had a two-run triple in a six-run sixth inning.
Cincinnati's Homer Bailey allowed four runs on nine hits and a walk in five innings.
Padres reliever Luke Gregerson also struggled, allowing five runs on four hits and a hit batter.