Newton overcame two interceptions in tossing for 263 yards while gaining 68 on the ground with a score for Carolina (9-3), which moved to within one-half game of NFC South-leading New Orleans.
The Saints play Seattle Monday.
Tampa Bay (3-9) had its three-game winning streak ended as rookie quarterback Mike Glennon finished with just 180 passing yards.
He lost a key fumble and threw an interception.
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