Third-string quarterback Josh McCown completed 20 of 29 passes for 157 yards and 2 touchdowns.
Allen also caught five passes for 51 yards and a TD. Booker caught four passes for 16 yards.
The Browns (2-2) and Bears (3-1) closed out the preseason for the ninth straight year. All teams must trim their rosters to 53 by Friday, and they can establish an 8-man practice squad by Saturday.
Veteran backup McCown got the start for the Bears and he directed an impressive drive on their first possession. Unfortunately, Robbie Gould missed a 35-yard field goal attempt wide left at the end of the 11-play, 52-yard drive. McCown completed 4 of 6 passes for 46 yards on the drive that came up empty.
It was the first field goal attempt Gould has missed in the preseason. He had been 7-for-7, including a game-winning 57-yarder.
The Bears regained possession when undrafted safety Jeremy Jones intercepted a Colt McCoy pass and returned it 13 yards to the Cleveland 30. On the next play, McCown passed 30 yards to Dane Sanzenbacher for a touchdown. Following a review by the replacement officials, the play stood. Gould converted to make it 7-0.
Of Sanzenbacher's TD, coach Lovie Smith said: "(It's) Good for him. He has great hands. He had a good camp. We expect him to make those kinds of plays."
The Bears improved their lead to 14-0 when McCown passed 11 yards to Allen for a TD with 4:25 left in the half. The scoring drive covered 44 yards in five plays.
The Browns finally got on the scoreboard when QB Seneca Wallace passed two yards to Rod Windsor for a touchdown with 41 seconds left in the half. Phil Dawson converted to cut the Bears' lead to 14-7. The 80-yard scoring drive took eight plays.
McCown completed 16 of 20 passes for 137 yards and two touchdowns in the first half. His passer rating was 128.5.
Booker rushed for 48 yards on 7 carries as the Bears racked up 202 total yards. Allen also had five catches for 51 yards and one TD. Booker caught four first-half passes for 16 yards. Sanzenbacher had two catches for 34 yards and a TD.
In the second half, McCown was intercepted on the Bears' first possession. His sideline pass intended for Sanzenbacher was picked off by Tashaun Gipson.
The Browns' 5-play, 24-yard drive ended with a 39-yard field goal by Dawson to make the score 14-10.
Following a challenge of an incomplete pass intended for the Browns' Josh Gordon, the Bears' Greg McCoy was ruled to have intercepted a pass from the Browns' Thaddeus Lewis. McCoy was credited with a 15-yard TD return to make the score 21-10 in favor of the Bears. The deflected pass bounced off the foot of the Browns receiver Gordon instead of hitting the ground.
The Bears came right back for another quick score when Browns punter Reggie Hodges had his kick blocked.by Patrick Trahan. Brittan Golden returned the block 22 yards for a touchdown and the Bears led 28-10.
he Browns scored again after Lewis had an 18-yard run to the Bears' 1. From there, Adonis Thomas leaped into the end zone and the Bears led 28-17 with 10:12 left in the fourth quarter.
The Browns pulled to within 28-20 after a 42-yard field goal from Dawson with 5:02 left in the fourth quarter.
Following Thursday night's exhibition at Cleveland Browns Stadium, the Bears will direct full attention to their regular-season opener against the Colts at Soldier Field.