Carolina (4-8) won its first three games of the season but then lost eight in a row. The Panthers finally ended their slide against the Browns (6-6), who had won four of their previous five games to move within a half game of first place Pittsburgh in the AFC Central.
"We have been through quite a bit of adversity and this group has stuck together," Carolina Coach John Fox said. "I'm proud of our players and coaches. It was really good to see these guys with smiles on their faces. It's a huge gorilla off our back, not even a monkey."
Brown replaced Lamar Smith, who was put on paid leave Friday after a DWI incident. Brown ran 27 times in his first 100-yard game. He had just 119 yards on 27 carries in his first 10 games.
"Coach kind of hinted Friday I would start," Brown said. "I never prepare as a backup, I always prepare to be No. 1. Lamar went down and it was an opportunity for me to step up."
The Panthers had a 10-6 lead with 7 1/2 minutes left in the fourth quarter when linebacker Mark Fields hit Browns quarterback Tim Couch and forced a fumble.
Carolina recovered and got a clutch first down when Brown ran for three yards on fourth and one with 5:31 left.
"With fourth and one, Rodney (Peete) told me 'get behind your shoulders, get both hands on the ball and go get it,'" Brown said. "The Browns were giving up the left on the outside so we stuck to our game plan. They gave us something and we took advantage of it. If it works, don't change it."
Shayne Graham kicked a 44-yard field goal with 2:53 remaining to give the Panthers a 13-6 edge.
Emmanuel McDaniel sealed the victory with his second interception of the game on Cleveland's final drive after Andre Davis bobbled Couch's pass.
Couch completed 12 of 27 passes for 130 yards and three interceptions as the Browns managed only 233 yards.
"I thought we were going to have a great game offensively, but they are a great defense," Couch said. "There is a reason they are rated in the top 10 in defense."
"Things happened today that haven't happened to us in a long long time," Cleveland Coach Butch Davis said. "Previous games we've been able to get the ball in the red zone and score touchdowns instead of field goals. You make it extra difficult to win when you turn the ball over like we did today."
Cleveland struggled without leading receiver Dennis Northcutt, who left in the second quarter with a knee sprain.
"We really missed Dennis Northcutt today," Davis said. "When you lose somebody like that it makes it a little bit tough, but other guys have to step up and make plays."
Carolina has just 258 yards but scored the game's only touchdown on Rodney Peete's 24-yard pass to Wesley Walls with 23 seconds left in the first quarter.
Phil Dawson kicked a 33-yard field goal in the third quarter to bring Cleveland within 7-6. But Graham extended the lead for the Carolina with a 43-yarder 5:47 into the fourth.