Led by All-Pro end Myles Garrett, who had two sacks, the Browns held Tampa Bay without a point on its final seven possessions.
Brady completed 29 of 43 passes for 246 yards and was sacked four times.
Brissett, who began his career as one of Brady’s backups in New England, went 23 of 37 for 210 yards. Chubb finished with 116 yards on 26 carries.
Brady opened the second half completing his first six passes, including a 28-yarder to Mike Evans, who became the first Tampa Bay player to reach 10,000 yards receiving.
The Buccaneers took a 17-10 lead when Brady connected with rookie Ko Kieft on a 5-yard scoring pass. It was the 638th TD pass for Brady, and No. 1 for Kieft, who is listed as the team’s fourth-string tight end.
Security personnel spent part of the second half trying to capture a skunk, which was on the loose inside the stadium.
Video showed the critter walking up and down steps while trying to find an exit.
Garrett arrived for the game wearing a customized white suit accented with dinosaur fossils.
The outfit was a nod to Garrett recently being named a community service ambassador for the Cleveland Museum of Natural History. Garrett is a paleontology enthusiast.
Large circular rings of tire tracks were still visible on Cleveland’s field after an intruder broke into the stadium earlier in the week and drove a vehicle on the turf.
The unknown suspect, who broke into the stadium on Monday night, caused superficial damage and divots.
Police are investigating the incident, which forced the stadium’s maintenance crew to make repairs to get the surface game ready.
Buccaneers: RT Tristan Wirfs was carted off the field in OT after sustaining an apparent serious leg injury. Players on both teams knelt as he was being checked by medical personnel. ... S Antoine Winfield Jr. was evaluated for a concussion in the first half, but returned.
Browns: CB A.J. Green (head) left the field after making a low tackle late in the first quarter. An official noticed Green staggering and escorted him off. ... Garrett, who is still dealing with a shoulder injury sustained in a September car crash, spent time in a medical tent in the first quarter.
Buccaneers: Host New Orleans on Dec. 5.
Browns: Watson plays his first game in 700 days against the Texans, who drafted him in 2017.