Newton completed 4 of 9 passes for 65 yards and led a pair of touchdown drives in the preseason game before exiting late in the second quarter with Carolina (1-1) up 14-6.
Stewart ran for 26 yards on four carries and made a strong case to be the Panthers' goal-line back — if not their primary ball carrier — with scoring runs of 3 and 2 yards.
Carolina's first three possessions netted a yard and no first downs. Newton compounded the problem by overthrowing Kelvin Benjamin on a deep ball after the rookie receiver got behind the secondary.
But Stewart replaced DeAngelo Williams and immediately gave the Panthers a boost with a 17-yard carry around left end. The Panthers found their rhythm after that, driving 66 and 50 yards for touchdowns on their next two possessions.
"We had a slow start tonight, which is unacceptable," Newton said. "We have to stay on schedule and not waste opportunities like the shot to Benji. Kansas City's a good football team and we didn't match their intensity early, but it was good to put a few drives together and score some points."
The Chiefs (1-1) moved the ball well early on without star running back
Kansas City's search for a reliable No. 2 receiver continues.
Newton had to shake off some early rust.
He missed on five of his first six passes and was sacked for a 13-yard loss, leading to three straight three-and-outs to start the game. He didn't run the ball at all because coach Ron Rivera didn't want to chance him reinjuring his left ankle.
Carolina benefited from a 32-yard pass interference penalty on Chiefs cornerback
Newton connected on a 24-yard pass to Benjamin over the middle on Carolina's next series leading to Stewart's second score.
It was an encouraging return to the field for Stewart, a former first-round draft pick who has missed 17 games the past two seasons with foot and ankle injuries. Stewart has been limited to 516 yards rushing and one touchdown the past two seasons after rushing for 3,500 yards and 26 TDs during his first four seasons in Carolina.
"It's been a while since I've touched the end zone," said Stewart, who sat out the first preseason game because of a hamstring injury. "It's the preseason so it's good to get my feet wet and get back into the groove."
The Panthers had a chance to extend their lead before halftime, but Benjamin lost his cool and head-butted Chiefs defensive back