Chicago owned a 16-9 lead with time running down, but Hoyer led the Browns on a 76-yard march that ended with a 14-yard scoring throw to Dan Gronkowski with 6:47 to go. A two-point conversion pass was incomplete.
The Browns regained possession and marched 22 yards to set up Lanning's 32-yard field goals with 3:15 left.
Hoyer completed 24-of-35 passes for 307 yards, leading the Browns to their third exhibition win in four tries.
Robbie Gould kicked three field goals for the Bears and their only touchdown came when Jordan Palmer threw a 5-yard pass to Joe Anderson in the second quarter.
Chicago posted a 2-2 exhibition record.
The Bears will host Cincinnati to start the regular season on Sept. 8. Cleveland will also be at home that day against Miami.