Red closer Aroldis Chapman entered the ninth with 6-2 lead but allowed singles to the first three batters he faced. He struck out Anthony Rizzo and got another out but then walked in a run.
Wellington Castillo knocked in two more runs, getting the Cubs within 6-5. Chapman, who allowed four hits and two walks and three runs in 2/3 of an inning, walked Cody Ransom to again load the bases before being pulled.
Hoover came in and was able to close the game with a four-pitch strikeout of Darwin Barney. It was Hoover's first save.
Cincinnati's Joey Votto scored the game's first run and was part of Cincinnati's two-run sixth while Shin-Soo Choo, who drove in a run in the second, scored in the seventh and eighth innings to key the Reds' offense.
Cincinnati starter Mike Leake (2-1) took advantage of the offensive spurt and scattered nine hits over 5 2/3 innings to get the win.
But the Reds were up 4-0 by then and had hung the loss on Carlos Villanueva (1-2), who was charged with four runs. He allowed seven hits and walked two while striking out four in 5 2/3 innings.