The improbable victory means Baltimore veteran Ray Lewis — who says he'll retire at the end of the season — isn't done yet.
Meanwhile the Ravens' triumph brought a sharp end to quarterback great Peyton Manning's first season in Denver.
"Our team is so confident and everything went against us, but we found a way to come here together and we're leaving together," Lewis said afterwards.
"It's just awesome."
The Ravens advanced to the American Conference championship game, where they'll face either New England or Houston for a berth in the Super Bowl. The NFL championship spectacular will be played in New Orleans on February 3.
The visiting Ravens, who entered the game as 9.5 point underdogs, claimed victory after Tucker kicked a 47-yard field goal in the second overtime, six plays after Broncos quarterback Peyton Manning was picked off.
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.
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 defences came up strong in overtime, Manning, who threw for 290 yards and three touchdowns, was intercepted when Corey Graham superbly picked off a pass intended for Brandon Stokley.
With the win, the Ravens advance to the American Football Conference championship game on Jan. 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.
Then came the overtime drama which will haunt Manning and the Broncos through the off-season.
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.
Baltimore's Ray Rice rushed for 131 yards and a touchdown from 30 carries while receiver Smith had two touchdowns and 98 yards.
The loss represents 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 had plans for playing next week, guys were excited and to get beat in overtime by a field goal is really disappointing," Manning said.
"We made a lot of strides and accomplished a lot this season but it definitely stings ending in a loss like this.
"I accomplished a lot more this year than I certainly thought I would have personally and I think the team exceeded its expectations as well.
"We really didn't know what to expect from this team. It's hard to form chemistry when you have a lot of new players come in such a short space of time and we did that.
"This is a hard one to swallow but I'm certainly proud of this team and what it went through to get to this point."