After the Broncos struck first, Cleveland responded with a scoring drive on its first possession.
It began on the Browns 28-yard line, and running back Trent Richardson carried the ball on three of the first five plays to gain 18 yards.
To cross midfield, quarterback Brandon Weeden hit tight end Benjamin Watson for a first-down completion of 13 yards, and a play later the pair connected again for 15 yards.
Cleveland picked up one more first down and moved into the red zone, but on the following series, the drive stalled.
On third-and-goal from the 9-yard line, Weeden tried to hit wide receiver Josh Cooper, but safety Mike Adams – who spent the last five years in Cleveland – hit the receiver as the ball arrived to force an incompletion.
Kicker Phil Dawson converted on a 27-yard field goal on the next play to make the score 7-3 with 4:35 remaining in the first quarter.