The Bears took a 7-0 lead on their second possession of the game on running back Kyle Monangai's 8-yard touchdown run with 5:40 left in the first quarter. The rookie seventh-round pick powered into the end zone behind blocks by left tackle Theo Benedet and right guard Jonah Jackson.
The 8-play, 47-yard drive was highlighted by a pair of 15-yard completions from Williams to Odunze, including one on third-and-9.
The TD came after the Bears defense forced the Giants to turn the ball over on downs as defensive end Montez Sweat and linebacker Noah Sewell teamed up to sack Jaxson Dart on fourth-and-2 from the Chicago 49.
After the teams traded punts, the Giants tied the score 7-7 on Dart's 3-yard TD run early in the second quarter, capping a 6-play, 80-yard drive.
The Giants were in position to take the lead after advancing to the Bears' 19. On fourth-and-1, Dart's high pass in the end zone was snared by tight end Daniel Bellinger. But safety Jaquan Brisker deftly wrestled the ball away to force an incompletion, preserving the tie.
New York eventually took a 10-7 lead on Younghoe Koo's 32-yard field goal with :03 left in the first half. Dart completed passes of 21 and 25 yards to tight end Theo Johnson on back-to-back plays to set up the go-ahead kick.
The Giants increased their lead to 17-7 on Dart's 24-yard touchdown run on the opening possession of the second half.
New York was seemingly about to pad its lead, but Gardner-Johnson forced Dart to fumble on a designed run and Nahshon Wright recovered at the Chicago 16.
Dart sustained a concussion on the play, exiting in favor of veteran Russell Wilson.
The Bears converted the game's first takeaway into Cairo Santos' 22-yard field goal, cutting the deficit to 17-10 with :34 remaining in the third quarter.
On Wilson's first possession in place of Dart, the Giants marched 79 yards to the Bears' 1, where they settled for Koo's 19-yard field goal to take a two-score lead at 20-10 with 10:19 to play in the fourth quarter.
But the Bears followed with another heart-pounding rally, moving to 6-3 with the victory.