Carolina quarterback Young tossed two daring second-half touchdowns on fourth down to give the Panthers a precious win heading into the final sprint for postseason places.
The Rams - who boasted the best record in the National Football Conference heading into Sunday's duel in Charlotte - were left ruing mistakes at key moments.
Rams quarterback Matthew Stafford gave up a first-quarter interception that Panthers defender Mike Jackson returned for a touchdown before a costly fourth-quarter fumble effectively sealed his team's defeat.
The win leaves the Rams at 9-3 for the season at the top of the NFC West, while the Panthers improved to 7-6 to stay hard on the heels of the Tampa Bay Buccaneers in the NFC South. The Bucs remain top of the division after a 20-17 win over the Arizona Cardinals.
The Rams appeared to be poised to extend their winning run early in the fourth quarter when Stafford led a superb 89-yard touchdown drive to help give the visitors a 28-24 lead.
That scoring drive included an astonishing one-handed catch from Rams receiver Puka Nacua that set up a close-range rushing touchdown for Kyren Williams on the next play.
However, Young responded to that challenge with a gutsy 43-yard touchdown completion on fourth down to find Tetairoa McMillan and give the home side what turned out to be a decisive 31-28 lead after Stafford's late fumble.
Young, the No.1 pick in the 2023 draft who has struggled to find consistent form in his first three seasons in the NFL, said he had never had any doubt about attempting to convert his two fourth down touchdown passes.
"I just trust my guys; there's no big conversation, no big hoo-rah," Young said.
"I know these guys are always ready...I know who they are. I know the competitors they are. No matter what, I'll always have confidence in them, so that'll never change."
"I'm so proud of this group - the resilience, the finish, the ability to go blow for blow with an amazing team," Panthers head coach Dave Canales said afterwards.
Bills sink slumping Steelers
In other games, Josh Allen and the Buffalo Bills muscled their way to a 26-7 road win over Pittsburgh in a defeat that left Steelers quarterback Aaron Rodgers bloodied and bruised.
A miserable afternoon for Rodgers was summed up in a brutal sack by the Bills' Joey Bosa, which saw the veteran slammed face first into the turf before fumbling to allow Buffalo's Christian Benford to race in for a touchdown.
The win saw Buffalo improve to 8-4 in the AFC East, where they are chasing the New England Patriots (10-2) who host the New York Giants on Monday.
"We've got to find a way of winning these football games in this cold, winter type of night against a tough AFC North opponent - and we found a way," Bills quarterback Allen said.
Elsewhere, the San Francisco 49ers eased past the struggling Cleveland Browns 26-8 to remain firmly in the playoff hunt, improving to 9-4 to stay just behind the Rams in the NFC West.
The Jacksonville Jaguars (8-4) are also closing in on a playoff spot after a 25-3 win over the Tennessee Titans.
The victory vaulted the Jaguars into top spot in the AFC South after the Indianapolis Colts suffered a costly 20-16 reverse against the Houston Texans.