After the Cubs reached closer David Weathers (2-3) for five hits and two runs in the ninth, Hopper led off the bottom of the ninth against Bobby Howry (5-6) with a single to right field. Pinch-hitter Juan Castro sacrificed Hopper to second, and Encarnacion singled between diving third baseman Aramis Ramirez and the bag for the winner.
Encarnacion also homered and Jeff Keppinger hit a two-run double as the Reds improved to 4-1 on their current homestand. They've won eight of their last nine at Great American Ball Park.
The Cubs, who entered Friday with the major leagues' best record (31-16) since June 3, have lost back-to-back games for the second time in less than a week. Chicago dropped two straight at Arizona last weekend.
Pitching through a middle-innings drizzle, Bronson Arroyo allowed two unearned runs and one walk while striking out five in 7 2-3 innings. He also hit a batter in winning for the second time in three starts.
Beginning with Derrek Lee's double-play ball that ended the second inning, Arroyo retired 12 consecutive batters before Mark DeRosa's two-out single to left in the seventh.
Ryan Theriot's two-out, run-scoring double drove Arroyo from the game. David Weathers came in to strike out Lee and pitch the ninth.
But Weathers couldn't notch his 21st save in 25 chances.
Ramirez led off the ninth with a single and Cliff Floyd grounded a single to right to move Ramirez to third. DeRosa then lined a single to left to score Ramirez. One out later, Jason Kendall tied the game with a single to left.
The Cubs took the lead in the first when Theriot's hit to right with one out skidded through Ken Griffey Jr.'s legs for a two-base error, allowing Theriot to reach third. He scored on Lee's sacrifice fly to give the Cubs a 1-0 lead.