Keenum exited at halftime in favor of Miller Moss after completing 9 of 17 passes for 119 yards and a 75.4 passer rating.
The Bengals opened the second half by extending their lead to 24-9 on quarterback Sean Clifford's 20-yard TD pass to receiver Noah Thomas.
McPherson's 58-yard field goal made it 27-9 early in the fourth quarter.
Defensive back Skylar Thomas generated the Bears' first takeaway, intercepting a Clifford pass at midfield. But Santos missed a 53-yard field goal try wide right.