DENVER -- In the end, the ball literally bounced Kansas City's way.
"Cairo, he kept us all in suspense with that bank shot, or the chip shot, or whatever it is," Chiefs coach Andy Reid said. "It was a great game to watch. I'm sure it put a couple of extra gray hairs on your head. Proud of our guys, our coaches and the job they did in all three phases."
Quarterback Alex Smith twice drove the Chiefs to within field-goal range in overtime and engineered the game-tying touchdown drive and two-point conversion in the final moments of regulation.
The Chiefs (8-3) overcame a three-touchdown performance by Broncos quarterback Trevor Siemian, including two scores in the fourth quarter, the last coming with three minutes left in regulation on a 76-yard pass to Bennie Fowler.
"It stinks to lose, especially going back and forth like that," Siemian said. "A couple of times I thought we had it. But really, hats off to Kansas City. I thought they battled and battled. They played a really good game."
The win gives the Chiefs a leg up on Denver (7-4) in the race for a playoff berth. Kansas City remains one game back of the AFC West-leading Oakland Raiders (9-2) with five games to play.
"It puts us in position. We know if we handle business, we'll be OK," Chiefs safety Eric Berry said. "It's a good win. I'm going to enjoy it, but we've got another game on Sunday."
Siemian drove the Broncos to a 44-yard field goal by Brandon McManus on the opening overtime possession. Smith responded by driving the Chiefs to the Broncos 19-yard line, where after a third-down incompletion, Santos came on to kick a tying 37-yard field goal with 4:19 left in the extra period.
Denver came back to try a 62-yard field goal that was well short, giving the Chiefs a final chance starting on the Broncos 48-yard line.
Considering the Broncos were unlikely to get the ball back and McManus connected regularly from beyond 60 yards in practice, Broncos coach Gary Kubiak decided to go for the lengthy field goal.
"My thing is that we're going to try to win around here," Kubiak said. "I made that decision, and it just didn't work out."
McManus said the kick was within his range but his lead foot struck the ground just before impacting the ball, messing up the field-goal try.
"From that distance, everything kind of needs to be perfect just because of how far you are away," McManus said. "It didn't happen for me."
Kansas City took over with just over minute remaining in the extra period. Smith quickly drove the Chiefs down to the 16-yard line, setting up Santos' winner.
"It's amazing," Santos said. "It's a huge game in primetime, and as a kicker, I ask for opportunities like these so I'm happy to come through for the team."
Smith moved the Chiefs to the Broncos 14-yard line in the final seconds of regulation, and an 11-yard pass on fourth down to Tyreek Hill gave Kansas City a first-and-goal at the 3.
Smith found Hill again on a pass in which the receiver initially was ruled down at the 1. However, a replay review found Hill crossed the goal line for the score with 12 seconds left in regulation.
Demetrius Harris caught a pass from Smith for the two-point conversion, sending the game into overtime tied at 24.
Siemian completed 20 of 34 passes for 368 yards. Smith was 26 of 44 for 220 yards and one touchdown. Neither was intercepted.
Kansas City tight end Travis Kelce made eight receptions for 101 yards. Denver wide receiver Emmanuel Sanders caught seven passes for 162 yards and a touchdown.
NOTES: Broncos LS Casey Kreiter was among the team's inactive players because of a calf injury. Earlier in the week, Denver signed veteran LS Thomas Gafford to fill in for him. ... Broncos DL Derek Wolfe was back in the lineup after he missed last week's game with an elbow injury. He had eight tackles, including a sack. ... Chiefs WR Jeremy Maclin missed a third consecutive game because of a groin injury. ... Also inactive was Chiefs OLB Dee Ford, who missed part of last week's game after sustaining a hamstring injury. Ford has 10 sacks this season. ... Chiefs DE Rakeem Nunez-Roches started in place of injured DE Jaye Howard, who was sidelined by a hip flexor injury. ... The game was originally scheduled for an afternoon start but was flexed by the NFL to a primetime matchup.