Young's 54-yard pass to Tommy Tremble set up the winning kick for Carolina (6-5), which completed its sweep of NFC South rival Atlanta.
The Panthers moved to within one-half game of first-place Tampa Bay in the division following the Buccaneers' 44-32 loss to Buffalo.
Young completed 31 of 45 passes with three touchdowns despite being escorted to the locker room late in the first quarter with a right ankle injury. He missed only one snap.
"I was able to come back and get re-taped," Young said. "Regardless, I just wanted to be back with my guys. I don't take these games for granted. You know, the Lord blessed me to be here, to have this opportunity. And any time that I am able to go, I always want to do that. So in the moment, you're just working through pain."
Young threw a go-ahead 12-yard touchdown pass to Tetairoa McMillan with 1:08 remaining to give Carolina a 27-24 lead. But Zane Gonzalez kicked a 45-yard field goal for Atlanta with 16 seconds remaining to force overtime.
The Falcons (3-7) suffered their fifth straight loss, including back-to-back overtime defeats.
"We got to find a way to make plays," Falcons coach Raheem Morris said. "I keep saying it every single week: Somebody's got to make a play at the end, whether it be offense, defense or special teams. We had some opportunities and were not able to get it."
Bijan Robinson ran for 104 yards and two touchdowns, but the Falcons couldn't overcome the loss of Michael Penix Jr. to a knee injury in the third quarter. Backup Kirk Cousins couldn't move the offense in overtime.
McMillan had eight catches for 130 yards and two touchdowns.
Young's go-ahead scoring pass was set up by Rico Dowdle's 28-yard run to the 10. A replay review ruled that Dowdle stepped out of bounds on what was initially ruled a 38-yard touchdown run by the officials.
Atlanta's secondary was short-handed with cornerbacks Dee Alford and Mike Hughes inactive. Young and the Panthers targeted fill-in cornerback Natrone Brooks often, including on Young's 36-yard scoring pass to Xavier Legette in the third quarter, cutting Atlanta's lead to 21-16.
Brooks then fumbled the kickoff return, giving the Panthers the ball at the Atlanta 32. Young was stopped by Kaden Elliss on a fourth-down run from the Atlanta 8. Fitzgerald's 34-yarder late in the third quarter pulled the Panthers to within two.
Penix left in the third quarter with a left knee injury, with Atlanta leading 21-16. Penix missed the Falcons' 34-10 loss to Miami on Oct. 26 with a bone bruise on his left knee.
Penix completed 13 of 16 passes for 175 yards after struggling with accuracy in last week's 31-25 overtime loss to the Indianapolis Colts in Berlin.
The Panthers had an injury scare late in the first quarter when Young remained down after being sacked by Billy Bowman Jr. for a loss of 8 yards. Young eventually walked off the field and was escorted to the locker room, and was announced by the team as questionable to return with an ankle injury.
Backup Andy Dalton replaced Young for only one snap, a holding penalty, early in the second quarter, before Young was back on the field, his right ankle taped.
Young was 7 of 8 for 67 yards, including a 7-yard scoring pass to McMillan, on Carolina's opening drive. The strong start gave him half of his full-game total of 124 yards passing in last week's 17-7 loss to New Orleans.
Carolina rallied after trailing 21-7 in the second quarter.
"It's part of our identity; we embrace that," Young said. "It's just resilience. We talk about it. Whatever it was, it's on to the next play."
Cam Newton held the previous Carolina record with 432 passing yards against Green Bay on Sept. 18, 2011.
"It's definitely an honor. I have so much respect for Cam and all he has accomplished," Young said. "To be able to be mentioned with Cam, it's definitely an honor."
The Panthers next visit San Francisco in a Monday night game on Nov. 24.
The Associated Press contributed.