The Panthers racked up 17 straight second-half points to improve to 2-0.
Stewart ran for a 4-yard touchdown late in the third quarter and scored from 1 yard with 3:52 remaining in the game. The touchdowns were Stewart's first in the NFL.
Carolina's Jake Delhomme passed for 128 yards and was intercepted once.
Brandon Lloyd caught five passes for 66 yards and scored a touchdown on a blocked punt for the Bears (1-1),