DENVER — One of the most storied NFL playoff teams ran into a rejuvenated Tim Tebow and the Denver Broncos.

Sorry, Pittsburgh Steelers.

The magic is back.

Tebow connected with Demaryius Thomas on an electrifying 80-yard touchdown pass on the first play of overtime and the Broncos defeated the stunned Steelers 29-23 in the AFC wild-card game on Sunday. Wild doesn’t begin to describe it. The play took 11 seconds and was the quickest ending to an overtime in NFL history.

Thomas hauled in a high play-action pass at the Denver 38, stiff-armed Ike Taylor and then outraced Ryan Mundy to the end zone. Tebow, who looked as startled as everyone else, chased down Thomas and knelt on one knee — a gesture known far and wide these days as Tebowing. Then he pounded a fist in triumph and took a victory lap.

“When I saw him scoring, first of all, I just thought, ‘Thank you, Lord,”’ Tebow said. “Then, I was running pretty fast, chasing him — Like I can catch up to D.T! Then I just jumped into the stands, first time I’ve done that. That was fun. Then, got on a knee and thanked the Lord again and tried to celebrate with my teammates and the fans.”

Prodded by John Elway to let the ball fly, Tebow acted as if the last three weeks never happened, lifting the Broncos to their first playoff win in six years.

Behind Tebow’s 316 yards passing, the Broncos (9-8) are heading to New England for a second-round game against the top-seeded Patriots on Saturday night. And, unlike Elway, who lost his first postseason start — to the Steelers at home in 1984 — Tebow is 1-0 in the playoffs.

“We’re just a fighting team. A lot of resilience,” Broncos cornerback Champ Bailey said. “In any adverse situation, we’ll find a way to get out of it. Everybody says we backed into the playoffs, we’re in. We did something right along the way. We’re in it. We won a game. Now, we’ve got to go try to win another one.”

The Steelers (12-5) lost despite Ben Roethlisberger rallying injury-depleted Pittsburgh from a two-touchdown halftime deficit with 10 points in the final 10 minutes.

Pittsburgh called tails for the overtime coin toss, and it came up heads.

Tebow, who engineered five fourth-quarter comebacks and three OT wins in the regular season, wasted no time in finding Thomas to end the game. Mundy was playing in place of Ryan Clark, the Steelers’ leading tackler who sat this one out because of a blood condition that’s exacerbated at altitude.

Clark was one of several Steelers sidelined or injured. Pro Bowl center Maurkice Pouncey was out, replaced by Doug Legursky, who had a bad snap right before halftime that moved Pittsburgh out of field goal range.

Thomas raced down the Broncos sideline, sending the crowd, including Elway, the Broncos executive vice president, into a frenzy at Sports Authority Field, which was rocking like the old Mile High Stadium back in the 1990s.

And Elway, the architect of so many those magical moments at the old place, jumped for joy on the field like he used to when he was the one throwing the winning pass.

The Patriots walloped the Broncos 41-23 last month, sending Tebow into a funk that included seven turnovers and a 40 percent completion clip — and prompting Elway to implore him to “pull the trigger” in the playoffs.

Did he ever.

Tebow completed 10 of 21 passes but Thomas hauled in four of them for 204 yards after his top target, Eric Decker, was lost to a left knee injury on the first play of the second quarter when he was hit by linebacker James Harrison.

Tebow also ran 10 times for 50 yards.

“I think we executed a little bit better. We tried to step up,” Tebow said. “We knew it was win or go home. This team wanted to fight. We wanted to play another game.”

These two teams had played the first ever regular season overtime game on Sept. 22, 1974, in Denver. Now, they played the first non-sudden death playoff game in history. The new rules called for both teams to get the ball in the extra period providing there wasn’t a touchdown by either the offense or defense.

Tebow took care of that in a hurry.

Making his first appearance in the playoffs after going 7-4 as Denver’s starter, Tebow outdueled Roethlisberger, a two-time Super Bowl winner who fell to 10-4 in the playoffs.

The Broncos snapped a three-game losing streak that had many wondering if they were even worthy of their first playoff in six seasons, and it kept the Steelers from their 34th playoff win, which would have broken a tie with the Cowboys for the most ever.

Tebow led Denver to 20 second-quarter points — they had scored just 13 in the quarter in his 11 starts — but a 20-6 halftime lead didn’t last long.

Receiver Mike Wallace had a 1-yard TD run, Shaun Suisham kicked a short field goal and Jerricho Cotchery grabbed a 31-yard TD pass with 3:48 left in regulation to tie it.

The Steelers were nearing field goal range in the final minute of regulation but the Broncos sacked Roethlisberger three times on that final drive, forcing a fumble the quarterback recovered.

“We were moving it and we had a shot,” Roethlisberger said. “Someone got, it felt like a finger, on the ball and knocked it out. After that, you’re trying to throw a 70-yard Hail Mary and that’s hard.”

Pittsburgh caught a break in the second half when the Broncos thought they had another takeaway inside the Steelers’ 20-yard line, but an errant whistle negated the turnover and the Steelers capitalized with an 87-yard TD drive to pull to 20-13.

Denver’s decision to defer upon winning the first-half coin toss started to look like a bad decision when Roethlisberger drove the Steelers to two quick field goals and the Broncos managed just 8 yards in the first quarter.

The Broncos’ bugaboo has been the second quarter, too, where they scored just 13 points in Tebow’s 11 starts, and things started off ominously when his top target got hurt on the first snap of the second quarter.

Linebacker James Harrison’s low tackle sent Decker out with a left knee injury, and the hard hit also broke up his 21-yard catch, which would have marked Tebow’s first completion.

As Decker — whose girlfriend, country singer Jessie James, performed at halftime — hobbled to the locker room, Tebow hit Thomas for a 51-yard gain down the left sideline, then found Eddie Royal for a 30-yard touchdown toss that gave the Broncos a 7-6 lead.

That was Denver’s first touchdown drive in 22 possessions.

Thomas’ 58-yard reception set up Tebow’s 8-yard dart into the end zone that made it 14-6.

The Broncos dialed up the pressure on Roethlisberger and rookie safety Quinton Carter’s interception at the Pittsburgh 18 set up Matt Prater’s first of three field goals, putting them up 17-6.

Roethlisberger was picked off on his next throw by Andre’ Goodman, but that interception was negated by Elvis Dumervil’s offside penalty. After a punt, however, Tebow connected with tight end Daniel Fells for 40 yards to the Steelers 25-yard line, setting up Prater’s second short field goal that gave Denver a 20-6 halftime lead.

The Steelers were driving for a score just before the break when a bad snap by Legursky lost 23 yards and took them out of field goal range.

This was just the Broncos’ second playoff win since Elway retired following his second straight Super Bowl triumph in 1999, and their first since Jan. 14, 2006, when the Broncos handed Tom Brady his first playoff loss.