Bolton delivered a 86-yard scoop and score to give the Chiefs a lead they would not relinquish in the fourth quarter after Melvin Ingram's tackle forced a fumble from Broncos running back Melvin Gordon.
The result means the Chiefs (12-5) will claim the AFC top seed if the Tennessee Titans (11-5) fail to beat the Houston Texans on Sunday.
The victory was also the Chiefs's 13th straight road win against AFC West opponents.
Mahomes completed 27 of 44 passes for 270 yards with two TD passes for Travis Kelce in the first quarter and Jerick McKinnon in the third. The Kansas City QB also rushed 54 yards from nine carries.
The Broncos, who will finish last in the AFC West with a 7-10 record, were difficult to shake all game, with QB Drew Lock rushing two touchdowns, while running back Gordon scored a 47-yard TD to put them up 20-17 in the third.
The Chiefs found the match-winning play in the fourth quarter as the Broncos closed the nine-yard line after a 10-play drive with Ingram forcing the error and Lock unable to tackle Bolton.
The Chiefs improved their record to 12-5 with Saturday's 28-24 win over the Denver Broncos, which was Kansas City's 13th straight road win against AFC West opposition.
The result means the Tennessee Titans have to beat the Houston Texans on Sunday to move above the Chiefs to claim the AFC's top seed.
"We'll watch the game and everything like that," Mahomes told ESPN after the game.
"We handled our business today. We'll see what happens tomorrow. Regardless we'll be ready to win some football games."
The Chiefs may have clinched the top seed on Saturday had they not gone down 34-31 to the Cincinnati Bengals last weekend, snapping their eight-game win streak.
Mahones, who threw two touchdowns and completed 27 of 44 passes for 270 yards, said the Chiefs needed to improve if they were going to make a long playoffs run.
"We've got to be better. We've got what it takes," Mahomes said.
"We've got everybody in the locker room to do what we want to do but we've got to be better if we want to make a run through the AFC because it's a tough division."
The Chiefs appeared in danger of a loss to the Broncos until ex-Los Angeles Chargers linebacker Melvin Ingram's tackle on Broncos running back Melvin Gordon forced a fumble which rookie Nick Bolton scooped and scored from in the fourth quarter.
"That was a heck of a play by Melvin Ingram," Mahomes said. "That's the reason why we got him here. He makes plays like that."
Knee injuries limited the edge rusher to just seven games in the 2020 season, his final campaign with the Los Angeles Chargers.
He did not register a sack last year but the 32-year-old Ingram has been a consistently productive pass rusher in his career.
Ingram is one sack shy of 50 at the NFL level and should be in a good spot to reach that milestone playing for a Steelers defense that features one of the league's best pass rushers in T.J. Watt.
Watt led the NFL in sacks with 15 last season and was first among edge rushers with a pressure rate of 25.8 per cent.
The attention Watt commands could free up Ingram to regularly wreak havoc in the backfield and revitalise his career in Pittsburgh.
Ingram told ESPN's Josina Anderson: "I definitely feel like it's the place for me.
"I met with coach [Mike] Tomlin. You can tell he's very involved and a players' coach. That's what stood out to me.
"He wants to win and that is what I am on. My role is my role. He just told me to come in and be me. Everyone knows how I play."
The Steelers sent Ingram to the Chiefs in exchange for a sixth-round pick in next year's draft.
Ingram was in his first season with the Steelers, having spent nine years with the San Diego/Los Angeles Chargers.
He tallied 25 pressures for the Steelers this year, third on the team behind Cameron Heyward (42) and T.J. Watt (27).
However, Ingram had reportedly stated a desire for more playing time, which he will now hope to get for a Chiefs defense that has struggled for much of 2021.
Asked about the deal, Steelers head coach Tomlin said: "I enjoyed working with Melvin. it just didn't work out the way we envisioned, the way he envisioned.
"What the team needs is first and foremost. But from a team perspective, it's better to have volunteers than it is to have hostages."
