Walker caught three passes for 37 yards on the drive, including a sensational 15-yarder along the sideline on the first play that was originally ruled incomplete before a replay review overturned the call.
Bagent played the entire second half, connecting on 20 of 28 passes for 212 yards with three TDs, no turnovers and a 128.9 passer rating.
The Chiefs took a 7-0 lead on the game's opening possession on running back Isiah Pacheco's 2-yard touchdown run, capping an 8-play, 69-yard drive.
Patrick Mahomes completed 2 of 5 passes for 31 yards. Kansas City's longest gain came when cornerback Nahshon Wright was penalized 14 yards for pass interference and 15 yards for a facemask on the same play.
The Chiefs increased their lead to 10-0 on Harrison Butker's 31-yard field goal. The kick was set up by Mahomes' 58-yard bomb to receiver Tyquan Thornton.
Kansas City then widened the margin to 17-0 on Mahomes' 4-yard TD pass to receiver Rashee Rice on the first play of the second quarter.
On their third possession of the game, the Bears cut the deficit to 17-3 on Cairo Santos' 28-yard field goal midway through the second quarter. Williams' 18-yard run to the Chiefs' 15 highlighted the 12-play, 61-yard drive.
Mahomes was then replaced by Gardner Minshew after completing 8 of 13 passes for 143 yards with one TD and a 124.8 passer rating. The Bears' No. 1 defense also yielded to the second unit following Kansas City's third possession.
Butker's 23-yard field goal made it 20-3 with 2:45 left in the first half. The kick came one play after cornerback Mekhi Garner broke up a pass intended for receiver Jason Brownlee in the end zone on third-and-goal from the 5.
After Williams' TD pass to Odunze late in the first half, the Bears had a chance to make it a one score game early in the second half, but Santos' 47-yard field goal attempt was no good, hitting the left upright.
The Chiefs followed by extending their lead to 27-10 on running back Elijah Mitchell's 2-yard TD run midway through the third quarter. The score was set up by quarterback Chris Oladokun's 50-yard pass to receiver Jimmy Holiday.
The Bears generated the game's first takeaway on defensive end Daniel Hardy's strip-sack of Oladokun. Defensive tackle Zacch Pickens recovered the fumble at the Chicago 41. Officials initially ruled that Oladokun was down, but coach Ben Johnson challenged the call, and it was overturned following a replay review.