The rookie signal-caller went 13-of-23 through the air en route to 149 yards and added 55 more on the ground for the Panthers (5-9).
The win was the third in four games for Carolina.
The Texans (10-4), meanwhile, saw their franchise-record, seven-game winning streak snapped.
Newton's fellow first-year quarterback T.J. Yates tossed a pair of costly interceptions for Houston, ending with 212 aerial yards.
Ray Liotta sues skin care company over use of likeness
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