With a smile that measured a mile wide, Denver quarterback Tim Tebow chased after his wide receiver, leaping into the crowd before taking a knee and praying. The endless debate on Tebow’s abilities as a quarterback had been drowned out by a raucous celebration, as Tebow circled the stadium, exchanging high-fives with Denver Broncos fans who were still trying to process what they’d just seen.

Challenged earlier in the week by John Elway, the team’s executive vice president, to “just pull the trigger,” Tebow responded in dramatic fashion Sunday with an 80-yard touchdown pass on the first snap of overtime to lift the Broncos over the Pittsburgh Steelers, 29-23, in the opening round of the NFL playoffs.

“We knew that it was win or go home,” Tebow said, “and this team wanted to fight. We wanted to play another game.”

On the first play from scrimmage in overtime, Tebow hit Demaryius Thomas mid-stride at the Denver 39-yard and the wide receiver did not stop until the Broncos had knocked the defending AFC champions from the playoffs.

Facing criticism and widespread skepticism about his ability, Tebow turned in the most memorable performance of his young career, throwing two touchdowns and rushing for another. Just one week after a dismal 60-yard passing performance against Kansas City, Tebow finished Sunday’s game with 10 completions in 21 passes for a career-high 316 yards, 204 of them on four receptions by Thomas.

“A lot is said, a lot was written,” Denver Coach John Fox said. “A lot of critique on him, and I thought he stepped up in a huge way tonight.”

Said running back Willis McGahee: “He showed he’s a quarterback in the NFL. Case closed.”

The win marked the Broncos’ second postseason victory since winning Super Bowl XXXIII in 1998 and first since 2006. It was also the latest in a series of 11th-hour heroics from a 24-year-old quarterback who had been increasingly maligned in recent weeks.

“They say he can’t throw, they say we wouldn’t be able to move the ball on them. We did that,” McGahee said. “I wonder what they’re going to say next week.”

With the win, the Broncos advanced to the second round of the playoffs and will visit New England on Saturday. The Patriots beat the Broncos, 41-23, on Dec. 18, snapping Denver’s six-game winning streak.

“We’re going to go as Tim goes,” said cornerback Chris Harris. “If Tim plays well, we’re going to keep winning. That’s how it is. The quarterback is the leader, and we’re definitely behind him.”

Sunday’s contest was the first playoff game to extend beyond regulation time since the NFL revised its overtime rules in 2010. But the new rules had no effect on the outcome.

Denver built a two-touchdown first-half lead, but the teams battled back and forth in the final two quarters before the Steelers took advantage of a critical Denver fumble. Steelers quarterback Ben Roethlisberger showed his own comeback artistry, hitting wide receiver Jerricho Cotchery with a 31-yard pass in the end zone to tie the game with less than four minutes remaining in regulation.

Denver won the coin toss in the extra period and needed all of 11 seconds to cap a dramatic week. The team had ridden a three-game losing streak into the postseason. Oddsmakers installed the visiting Steelers as the betting favorite by more than a touchdown.

In the first quarter, the Broncos’ offense managed only eight yards, all on the ground, and Tebow didn’t complete a pass. To make matters worse, on the opening play of the second quarter, Pittsburgh’s ferocious linebacker, James Harrison, knocked Denver’s leading receiver, Eric Decker, out of the game with a brutally legal leg tackle. But on the next play, Tebow hit Thomas with a 51-yard pass, and two plays later found Eddie Royal for a 30-yarder in the end zone.

The momentum swung instantly, and on the Broncos’ next possession Tebow again hit Thomas deep — this time for a 58-yard pass — before running in an eight-yard touchdown that gave the Broncos a 14-6 lead.

Tebow led the Broncos on four straight scoring drives. When the 15 minutes had mercifully ticked off the clock for the Steelers, the Broncos had gained 225 yards and scored 20 points in the second quarter. Tebow hadn’t thrown for more than 45 yards in the second quarter of any game this season. He had 185 Sunday.

“They came out and they played hard and we played hard, and it was a great game,” Tebow said. “And I’m very thankful we were able to get the win.”

More on the Broncos’ win:

Twitter reaction: Lady Gaga among those impressed

Under God: Tebow believers see John 3:16 in game stats

Summary and stats: Broncos 29, Steelers 23