It looked like the Broncos, who were 14-0 down in the first half, were finally beaten when they fell 24-17 further behind but a thrilling game ended with Bradley Roby capitalising on a fumble from Jamaal Sanders to earn Denver their second win of the season.
The two sides came into the game on the back of victories in the opening week of the season, but it was a frustrating start for both offenses.
Alex Smith suffered a similar fate in a scoreless opening quarter as he was twice sacked, before the hosts defended well on another Broncos drive to force the away team to punt at the start of the second.
The Broncos were left stunned when Kansas scored two touchdowns in less than three minutes, with Charles reaching the endzone first after benefiting from some impressive blocking on a 34-yard score.
As the visitors looked to recover from the setback, they were dealt another blow as rookie Marcus Peters, who was the 18th overall pick in this year's Draft, picked off a pass from Manning before carrying the ball 54 yards as the Chiefs claimed a 14-0 lead with Cairo Santos converting after both touchdowns.
A thrilling second quarter was far from over, though, as Manning finally found his range on the next drive before completing the series by spotting the blitz to find Emmanuel Sanders, who did the rest 16 yards from the endzone.
Aqib Talib produced an important defensive display as Kansas started their next drive by intercepting Smith's pass to get the ball back for the Broncos, who capitalised to get back on level terms before the half-time break.
Manning continued his recovery from a disappointing start by faking a handoff before finding Virgil Green, who completed the catch at the second attempt.
Despite the improvements from the Broncos offense, the Chiefs continued to make it difficult for Manning, who brought up 70,000 career passing yards, and his teammates as a tight contest continued.
Santos handed the Chiefs a lead with a field goal, before Brandon McManus cancelled out the score with a 54-yard effort late in the third quarter.
Much of the momentum appeared to be with Kansas in the second half, but poor decision on offense halted their progress on numerous occasions and brothers Britton Colquitt and Dustin Colquitt were busy early in the fourth quarter as their respective quarterbacks were sacked late in drives.
As the game entered the closing stages, Kansas were forced to run the ball with the threat of losing to a field goal, and they pulled ahead before the two-minute warning when Davis collected the handoff to evade DaMarcus Ware on the way to an eight-yard score.
Santos kicked the extra point to extend the lead to seven, but Manning produced a response by taking the Broncos the length of the field before finding Sanders on third down.
The drama was not over and it was the Broncos who completed a remarkable comeback as Charles fumbled on the first play after the Sanders touchdown, and Roby reacted quickest to collect the loose ball and reach the endzone to clinch the win for Denver.