Zack Cozart hit a two-run homer for Cincinnati, which took two of three this weekend from the Cubs and has won 17 of its last 19 games at Wrigley Field.
Bailey (1-1) struck out eight while allowing six hits and three walks.
The Reds have won 10 straight when Bailey faces the Cubs. He is 7-0 in his last 10 outings against Chicago and 5-0 in his past six at Wrigley Field.
The Cubs have lost six of their last seven.
Carlos Villanueva (1-4) was tagged for five runs and nine hits in 4 2-3 innings.