The 19-yard scoring play with 7:58 left in the game lifted Chicago (1-0) to a season-opening victory in its first game under Marc Trestman, who became just the fourth Bears head coach to win his first contest.
Trestman replaced the fired Lovie Smith after the Bears failed to make the playoffs last season.
Cutler completed 21-of-33 passes for 242 yards, two touchdowns and an interception. His favorite target was Marshall, who made eight grabs for 104 yards.
Matt Forte paced Chicago's rushing attack with 50 yards on 19 carries.
Andy Dalton went 26-of-33 through the air for the Bengals (0-1), compiling 282 yards with two touchdowns and two interceptions.
A.J. Green ended with nine receptions for 162 yards and both Cincinnati touchdown catches.