Soler, a 22-year-old prospect from Cuba, got a nine-year, $30 million deal from the Cubs. He was called up on Wednesday, started in right field and batted fifth.
After Luis Valbuena led off the second inning with a homer off Mat Latos (5-3), Soler hit a 2-1 pitch into the Reds' bullpen in center field.
Soler also had an RBI single off Jonathan Broxton in the eighth, cutting it to 6-5. Latos pitched into the eighth and gave up four runs while fanning a season-high 10 batters.
Aroldis Chapman escaped a two-on threat in the ninth for his 28th save.
Jacob Turner (4-8) made his first start for the Cubs and lasted only 3 2-3 innings.