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.
Toddler uninjured after being knocked over by Obama family dog
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'