Manning was picked off twice in the second half but he recovered to lead the Broncos on two late scoring drives -- the first capped by a go-ahead, 1-yard TD pass to Joel Dreessen with 11:47 remaining.
Manning went 27-of-35 through the air for 291 yards as AFC West-leading Denver (5-3) won its third straight.
Eric Decker made eight grabs for 99 yards with a pair of TDs and Demaryius Thomas collected six passes for 77 yards in the victory.
The Bengals (3-5), meanwhile, continued to struggle, dropping their fourth straight as Andy Dalton went 26-for-42 for 299 yards with a touchdown and interception.
Swim Week Miami Beach 2014 [PHOTOS]