Alex Smith threw for 202 yards and a touchdown with an interception, while tight end Travis Kelce, who was his main target on Monday night, pulled in seven catches for 133 yards and the score.
“To lose two in a row, for us it was all about just getting back on track,” Smith said after the AFC West showdown.
“Let’s just get back and rebound. We had two losses in five days, so for us, let’s just get back on track.”
Marcus Peters opened the scoring for Kansas City when he returned a fumble 45 yards for a touchdown early in the first quarter, as the home side raced out to a 14-0 lead midway through the opening period.
Denver quarterback Trevor Siemian was intercepted three times, as he went 19 of 36 for 198 yards and a touchdown.
“We had plenty of time, I was just trying to get something going,” Siemian said.
“We had plenty of time. I don’t need to be making stupid throws like that.”
After trailing 20-3 early in the third quarter, the Broncos (3-4) cut the deficit to 20-13 at the end of that period, before Butker kicked three consecutive field goals to halt any thoughts of a comeback by Denver, which was losing for the third straight time.
“Tonight, our defense played winning football in my opinion,” Broncos coach Vance Joseph said. “Our offensive line blocked.
“We ran the ball for 177 and the pass (protection) was better. But it all falls back to turning the ball over five times.
“That’s insane. You can’t win turning the ball over five times.”
Kansas City, which swept the Broncos in two games last season, was beating its opponent for the fourth straight time.
A.J. Derby caught a touchdown pass and Devontae Booker rushed for another score for Denver, which turned the ball over five times.
The Chiefs could have scored even more, but failed to convert on three trips inside the red zone and had to settle for field goals.
“I thought that was the big difference,” Smith said. “Missed opportunities in the red zone, lot of field goals obviously.
“If we’re able to capitalize and finish one of those off, it’s a different story, I felt like.”