Just then, linebacker Wesley Woodyard reached out in desperation and tugged on his right arm. The ball popped loose and Elvis Dumervil smothered it at the Broncos 34.
"He gashed us on that play, and somehow I just had to make a play," Woodyard said. "That's what it's all about, making plays at the end of the game."
That's something the Broncos (8-5) have perfected.
Tebow drove the Broncos downfield and Matt Prater, whose 59-yard field goal with 3 seconds left in regulation tied it, booted a 51-yarder with 8:34 left in overtime to give Denver an improbable 13-10 win.
"If you believe," Tebow said, "then unbelievable things can sometimes be possible."
Prater's third straight walk-off field goal gave the Broncos their sixth consecutive win and moved them into sole possession of first place in the AFC West at 8-5, a game ahead of Oakland.
Tebow improved to 7-1 since taking over as the starter in Denver, and six of those wins have involved second-half comebacks, five of them necessitating fourth-quarter rallies, three of which went to overtime.
No other quarterback in NFL history has produced six fourth-quarter comebacks in his first 11 NFL starts.
Broncos coach John Fox said Tebow has "competitive greatness. He wants the ball in clutch time."
After failing to score on their first dozen possessions, the Broncos faced the possibility of their first home shutout in the team's 52-year history. Instead, they erased a 10-0 deficit in the final 2:08 of regulation.
"I think we're rewriting the book on 'keep fighting,'" Fox said. "Our guys never blink. They remain positive. As bad as it looked today — we didn't play well; we had some drops. But the guy who dropped a couple of passes caught the ... touchdown. That's kind of the M.O. on this bunch."
Tebow threw a 10-yard touchdown strike to Demaryius Thomas, who had three drops, and then got the ball back with 53 seconds left after Barber saved the Broncos precious time by going out of bounds when the Bears were trying to run out the clock.
Denver was out of timeouts after Thomas' touchdown and had to try an onside kick, which the Broncos couldn't recover. But on second down after the two-minute warning, Barber cut outside and was pushed out, stopping the clock.
"That's usually something that never happens with a veteran running back," Woodyard said. "It's just like things go our way."
Barber wasn't around after the game to talk about his blunders.
"We all know what type of player Marion is," Bears coach Lovie Smith said. "All running backs are trying to get a couple more yards here and there. But we have to know the situation. In that situation, we have to be able to keep the ball inbounds. He'll tell you that. I know we'd all like to have that one back."
The Bears would have to punt, and Tebow got the ball back at his 20 and went to work, not needing to go far with Prater's strong leg in the thin air. He drove the Broncos 39 yards for Prater's kick, which he rocketed through the uprights to tie it at 10.
The Bears (7-6) won the toss in overtime and quickly got into field goal range before Barber, who rushed for 108 yards but will be remembered for his two late mistakes, coughed up the football.
"He was making a tough run, trying to get extra yards," Hanie said. "It's unfortunate. You want to stay in right there but that didn't lose the game for us. We lost it by not generating more points."
Tebow, who also led Denver to wins in OT at Miami and San Diego, took the Broncos from their 34 to the Chicago 33, and Prater sent the stadium into delirium.
The Bears, whose playoff hopes are faltering, are 0-3 since Hanie replaced an injured Jay Cutler, the former Broncos QB who has a broken thumb on his throwing hand and is out indefinitely.
With Matt Forte sidelined by a knee injury, Barber broke a scoreless tie in the third quarter with a 9-yard touchdown run and added a 16-yard gain on a screen to set up Robbie Gould's team-record 57-yard field goal on the first snap of the fourth quarter.
"We gave it away," Devin Hester said. "We were up 10 points."
That's not enough when Tebow's around.
"Those last five minutes, if it's within reach for us to get it, we feel like we're going to win," Woodyard said. "For all the Tebow haters: You'd better start believing."
Notes: The Broncos lost SS Brian Dawkins (neck), DB David Bruton (ankle), CB Andre' Goodman (concussion) and FB Spencer Larsen (hamstring). ... Denver ensured itself of avoiding two consecutive losing seasons for the first time since 1971-72, something that seemed unlikely when they were 1-4 with Kyle Orton at QB.
Follow AP Pro Football Writer Arnie Stapleton on Twitter: http://twitter.com/arniestapleton