Green, a backup running back, scored the winning touchdown with 1:38 left by stretching his 5-foot-8 frame as far it would go and barely extending the football over the goal line.
Green's long-armed effort capped a 60-yard drive and gave the Bears, who had to rally twice in the fourth quarter, a hard-fought 31-27 victory.
"I was definitely in," he said. "Once I got close I said, 'Don't hold back.' "
The Panthers (0-5) seemed so close to their first-ever victory when Eric Guliford returned a punt 62 yards for a touchdown with 2:37 left, giving Carolina a 27-24 lead.
But Erik Kramer, who was 23 for 41 for 259 yards and three touchdowns, then led the Bears downfield from their 40 in 10 plays, completing four passes for 48 yards, including one to Jeff Graham that gained 14 yards to the six.
Green carried five yards to the one, and then, after an incomplete pass, Green reached out for his touchdown as he was hit by Lamar Lathon, who was called for a face mask penalty on the play.
Kramer earlier threw two one-yard touchdown passes, using a play fake to allow his receivers to get wide open.
The Panthers used two big plays, the punt return, and a sack and fumble recovery for a touchdown by nose tackle Greg Kragen to twice take the lead in the fourth quarter.
Kramer had not been sacked in 104 pass attempts until Kragen broke through the line, hit Kramer's arm as he was trying to pass, then jumped on the ball at the one and crawled into the end zone.
The play, with 13:52 remaining, stunned the crowd at Soldier Field and gave the Panthers a 20-17 lead against the sluggish Bears (3-2).
Nate Lewis returned the kickoff 34 yards and Kramer then took the Bears 51 yards. He connected with Green on a key third-down pass of 14 yards and then on a third and goal from the one, he faked and flipped the scoring pass to Ryan Wetnight with 9:22 left, giving the Bears a short-lived 24-20 lead that was erased by Guliford's punt-return touchdown.