The Buccaneers trailed in the final minute of regulation.
In overtime, the Bucs lost one of their best players, tackle Tristan Wirfs, who was carted off with a leg injury.
With a Nick Chubb touchdown and a 45-yard pass play from Jacoby Brissett to Amari Cooper in overtime, Cleveland defeated the Buccaneers 23-17.
The offence of Tampa Bay (5-6) struggled to score consistently, while the defence was unable to win the game in the dying seconds.
Cleveland rallied for the game-tying touchdown with 32 seconds remaining, thanks to tight end David Njoku.
On fourth down, Njoku makes a leaping one-handed catch in the end zone to tie the game at 17-17.
After being kept out of the end zone since the first drive, the Browns had travelled 46 yards in less than two minutes to tie the game.
With 0:08 remaining in regulation, the Buccaneers reached the 48-yard line of Cleveland but were unable to move any closer for the game-winning field goal.
Brady's last-second heave at the goal line was incomplete, forcing overtime.