In the first game in NFL history where both sides scored more than 50 points, the Rams took the early advantage with two touchdowns in the opening 10 minutes.
The two sides went into the game with 9-1 records, tied with the New Orleans Saints for best in the league.
With both sides' offences too strong for their opponents' defence, both sides shared six touchdowns and a field goal to go into the half tied at 23-23.
The scoring continued into the second half, Mahomes hitting Tyreek Hill with a pass for a 73-yard score early in the fourth to make it a 40-37 game.
Jared Goff's fourth touchdown pass of the night was the most important: Mahomes hit Chris Conley to put the Chiefs up by four with 2:50 left to play, but Goff led the Rams back and connected with Gerald Everett for a 40-yard score with less than two minutes on the clock.
Kansas, with a full complement of timeouts in the tank, headed downfield again needing three to force overtime.
But Mahomes was picked off on the LA 48 before the defence forced a Rams punt.
Again the first-round pick in 2017 was intercepted as he went deep with 25 seconds left on the clock, with Goff taking a knee to end the game.