Smith completed 20 of 30 passes for 181 yards before Nick Foles came in to start the third quarter. The defense strangled Chicago's offense, and the Chiefs (1-2) came away with the win after dropping their first two exhibitions.
Kansas City has one more tuneup against Green Bay before opening against San Diego on Sept. 11. But in what is generally the final dress rehearsal for the starters, the Chiefs dominated.
"I certainly feel like we're ready as far as game speed, as far as getting the trials, getting enough plays," Smith said. "I felt like we got in a lot of different situations -- the goal line, short yardage, red zone, got a little two-minute today. That's kind of what you want, I feel like, in the preseason."
Kansas City got two second-quarter field goals from Cairo Santos and a 1-yard touchdown run by Spencer Ware in the closing seconds of the half to take a 13-0 lead. But the score didn't reflect just how lopsided the game was.
The Chiefs outgained the Bears 239-20 in the half, had 16 first downs compared to Chicago's two and dominated time of possession 21:54 to 8:06.
Kansas City had 177 yards passing compared to minus-7 for the Bears through the first two quarters.
Chicago's Jay Cutler had a rough game playing behind a line that was missing star right guard Kyle Long. The three-time Pro Bowl pick injured his shoulder at New England last week, forcing more shuffling for an already thin group.
Cutler played into the third quarter and completed 6 of 15 passes for 45 yards.
Alshon Jeffery had two catches for 18 yards and dropped a wide-open pass in the second quarter that could have led to a big gain. Kevin White had just a 3-yard catch, another quiet performance for the 2015 first-round draft pick.
He was taken from the field on a cart in the closing minutes of the game after Kansas City's Rakeem Nunez-Roches stepped on his leg following a pass to Josh Bellamy. Shaw screamed in agony and players kneeled as he was tended to on the field.
"Our thoughts and our prayers are with him and his family," said Fox, adding Shaw was "off to the hospital."
Chiefs: Coach Andy Reid on Smith: "I thought he had an opportunity to sling it around a little bit with those guys."
Bears: Cutler on the offense's struggles: "We're going to have a flux of guys kind of come into the lineup that we've been without the last couple weeks, which is going to help us, make us look a little more dynamic, a little more explosion out there."
Chiefs: Fifth-round pick Tyreek Hill caught a 58-yard pass from Foles in the third quarter that set up a touchdown.
Bears: The Bears held out OLB Leonard Floyd. The No. 9 pick in the draft, he has been dealing with a hamstring injury.
Chiefs: CB Phillip Gaines, working his way back from a torn ACL sustained last season, made his first preseason appearance but wasn't challenged. Gaines is in the running to start opposite Defensive Rookie of the Year Marcus Peters along with rookie D.J. White.
Bears: CB Tracy Porter was being evaluated for a concussion after taking a knee to the head from teammate Harold Jones-Quartey while tackling Demetrius Harris on a reception late in the second quarter. Jones stayed down for several minutes while being tended to by medical personnel before walking slowly toward the locker room.
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