The Chiefs had taken the lead on Harrison Butker's field goal with 5:57 remaining, but Bo Nix and the Broncos converted on a trio of third downs while marching right back down field. They proceeded to set up Lutz for the winner, but Leo Chenal was given credit for coming up the middle amid a big push by the Kansas City defensive line to get his hand on the kick.
Patrick Mahomes finished with 266 yards passing and a touchdown for Kansas City, which became only the fifth team to follow up a Super Bowl triumph by winning its first nine games. That also matches the best start to a season in franchise history.
The Chiefs' winning streak dating to last season is the longest in the NFL since the Packers won 19 in a row from 2010-11.
Travis Kelce had eight catches for 64 yards and a touchdown for Kansas City. DeAndre Hopkins caught four passes for 56 yards, and Kareem Hunt was held to 35 yards rushing but also caught seven passes for 65 yards.
Nix finished with 215 yards passing and two touchdowns for the Broncos (5-5). Courtland Sutton had six catches for 60 yards and a score, and his 13-yard reception on third-and-6 with 1:45 left gave Denver a chance to kick as time expired.