An error-strewn performance by Buffalo was ultimately decided by a pair of blunders on the final Denver drive as the home side hung on to a 22-21 lead.
Needing a field goal to win, Denver's hopes of victory were left hanging by a thread after quarterback Russell Wilson was sacked to take the Broncos out of field goal range.
But a costly pass interference penalty from Bills safety Taron Johnson on the next play moved Denver to easy kicking distance at the Buffalo 20-yard line.
As time ran down, Lutz looked to have blown Denver's chances of victory though when his 41-yard field goal drifted wide right.
Yet there was one last twist after officials spotted Denver had too many men on the field for Lutz's missed kick, allowing Denver to replay the field goal.
The second time, Lutz made no mistake, drilling the winning field goal through the uprights to give Denver a victory that leaves Buffalo's playoff hopes in the balance.
It marked the final act of a game that saw neither offence fully fire.
Buffalo's offence had got off to a stuttering start, coughing up a fumble on their first possession before quarterback Josh Allen tossed an interception on the Bills' next drive.
The Broncos defence forced Buffalo to punt away their next two possessions and Denver edged into a 9-0 lead after a Lutz field goal and a Courtland Sutton touchdown early in the second quarter.
Buffalo hit back however with their first effective drive of the match, Allen finding Dalton Kincaid for a 22-yard touchdown.
Allen made the two-point conversion to cut Denver's lead to one point at 9-8.
Another Lutz field goal from 49 yards put Denver 12-8 ahead before Allen's second interception of the night handed the ball back to the Broncos.
Denver were unable to take full advantage of the possession however, settling for another Lutz field goal from 40 yards to make it 15-8 at half-time.
Buffalo tied it up at 15-15 after Latavius Murray rushed over for a touchdown from three yards in the third quarter.
Denver hit back when Wilson cleverly flipped a pass to Javonte Williams with five minutes remaining in the fourth quarter for a close-range touchdown.
Crucially though Denver missed the extra point, allowing the Bills to take the lead for the first time in the game after Allen scampered over for a touchdown to make it 22-21 with just under two minutes left before Buffalo self-destructed on the final Denver drive to squander victory.
