The Panthers (5-3), who broke a two-game losing streak, established a 10-0 first-half lead with a 1-yard touchdown run by Jonathan Stewart and a 28-yard field goal by Graham Gano.
Overall, Newton was 18-of-32 passing for 154 yards. He rushed for 44 yards and was not sacked.
The Bucs (2-5), who lost their fourth straight game, were limited to a 41-yard field goal by Patrick Murray with 4:49 remaining in the third quarter.
The Bucs came into the game as the NFL's top passing team, but quarterback Jameis Winston was held to 210 yards on 21-of-38 passing. Winston threw two interceptions and lost a second-quarter fumble at Carolina's 33-yard line after being sacked by defensive end Julius Peppers.
For the first time in Winston's three-season NFL career -- 39 games, all starts -- the Bucs failed to score a touchdown. The Bucs were hampered by poor field position -- four of their drives began at the 17- 16-, 8- and 9-yard line -- but failed to take advantage of limited opportunities.
Carolina opened the scoring on its second possession, driving 82 yards on 17 plays while converting on five third-down situations. On third-and-goal, Stewart plowed over from the 1.
Late in the half, the Panthers drove 41 yards in nine plays and settled for Gano's field goal with 17 seconds remaining.
Tampa Bay's defense held Carolina to 254 total yards, but never sacked Newton. The Bucs have an NFL-low seven sacks in seven games.
NOTES: The Panthers were without inactive C Ryan Kalil (neck), who had missed two games earlier in the season, then aggravated the injury Oct. 22 at Chicago. Kalil was replaced by Tyler Larsen. ... Panthers G Trai Turner (knee) left in the third quarter. ... The Bucs had a depleted secondary as starting CBs Brent Grimes (shoulder) and Robert McClain (concussion protocol) were inactive.