Bellinger cranked a solo shot in the fourth inning and added a go-ahead, two-run single in the sixth as Chicago took the opener of a four-game series.
Ian Happ and Seiya Suzuki also went deep for the Cubs, who have won five of their last six games.
Chicago starter Jordan Wicks (2-0) picked up the win after allowing one run on five hits in five innings. He walked three batters and struck out three.
Daniel Palencia, Julian Merryweather and Keegan Thompson combined for four innings of one-run relief, with Thompson earning his first save of the season.
Noelvi Marte and Will Benson each had an RBI single for Cincinnati, which is 2-6 over its last eight games.
Nico Hoerner singled and Happ doubled to open the decisive sixth inning, chasing Reds starter Graham Ashcraft from the game. Lucas Sims entered in relief and Bellinger singled to right to plate Hoerner and Happ, giving the Cubs a 3-1 lead they wouldn't relinquish.
Ashcraft (7-9) gave up three runs on six hits in five-plus innings, walking one and fanning six.
Cincinnati had a chance to rally in the seventh when it put runners on the corners with one out, but Elly De La Cruz grounded into an inning-ending double play.
Suzuki made the Reds pay by hitting a solo shot with one out in the eighth inning to make it 4-1. Happ added a two-run blast in the ninth.
Benson forged the final score by driving in Marte with a base hit in the bottom of the ninth.
Ashcraft didn't allow a hit until Hoerner singled to lead off the fourth. Hoerner was thrown out trying to steal second as Happ struck out looking, but Bellinger followed with his solo home run to put Chicago up 1-0.
Cincinnati responded in the home half of the fourth, as Marte grounded his run-scoring single up the middle to level things at 1.
—Field Level Media