The visiting Ravens, who entered the game as 9-1/2 point underdogs, grabbed victory when Justin Tucker kicked a 47-yard field goal in the second overtime, six plays after Broncos quarterback Peyton Manning was intercepted.
Tucker's ice-cool kick in the freezing Mile High stadium ended a pulsating back-and-forth game that included a 90-yard punt return and 104-yard kickoff return for touchdowns from Denver's Trindon Holliday.
"That football game did the game of football proud," said Ravens head coach John Harbaugh, "It was one of the greatest football games you are ever going to see."
Denver were heading for victory in regulation until Ravens quarterback Joe Flacco threw a 70-yard touchdown pass to Jacoby Jones with 31 seconds left that tied the score at 35-35.
Then, after both defenses came up strong in overtime, Manning, who threw for 290 yards and three touchdowns, was intercepted for a second time when Corey Graham superbly picked off a pass intended for Brandon Stokley.
"A bad throw and the decision probably wasn't great either," said Manning.
With the win, the Ravens advance to the American Football Conference championship game on January 20, where they will play the winner of Sunday's game between the New England Patriots and Houston Texans.
The game was incident packed from the outset with Holliday opening the scoring with a spectacular punt return less than three minutes in. But Baltimore responded with quick touchdowns as Flacco found Torrey Smith with a 59-yard pass before Corey Graham intercepted Manning and ran in a 39-yard score.
Manning found Stokley with a 15-yard touchdown pass to tie the game at 14-14 after the first quarter.
The remaining three quarters followed the same pattern - a touchdown for Denver followed by a reply from Baltimore, ending with Jones's crowd-silencing score as he took advantage of some awful coverage from Denver safety Rahim Moore.
The Broncos had the ball with half a minute on the clock but chose to take the knee and go into overtime rather than try to make the ground needed for a field goal attempt.
Then came the overtime drama which will haunt Manning and the Broncos through the offseason.
The Ravens, with inspirational defensive leader Ray Lewis in his final season, were carried to victory by Flacco who completed 18-of-34 passes for 331 yards and three touchdowns.
"It puts Joe Flacco in the elite category where he deserves to be," said running back Ray Rice, who rushed for 131 yards and a touchdown from 30 carries while receiver Smith had two touchdowns and 98 yards.
The loss was be a bitter disappointment for Manning, who had been hoping for a Super Bowl appearance in his first season for Denver after missing last season with Indianapolis following several neck surgeries.
"We thought we were peaking at the right time but we played a good team," said Manning.
"A stout defense with a lot of veteran players. It’s very disappointing because of how much effort and hard work this team has put into this season."
Flacco acknowledged some good fortune, in the way that Jones was allowed to get open for the crucial game-tying touchdown.
"You have to get a bit lucky, it worked out and we were able to take a shot and everybody came through and when that opportunity arose, there is no way to explain it," he said.
"It was an awesome football game. It was just crazy."