KANSAS CITY, Mo. -- Coach Andy Reid had some simple advice for Patrick Mahomes when the Kansas City Chiefs faced long odds to beat the Buffalo Bills in Sunday night's divisional-round playoff game.

"When it's grim, be the Grim Reaper and go get it," Reid said he told Mahomes right before the quarterback brought the Chiefs back for a 42-36 overtime win that sends them to next weekend's AFC Championship Game against the Cincinnati Bengals.

"He did that," Reid said. "He made everyone around him better, which he's great at, and he just does it effortlessly. When it gets tough, he's going to be there battling."

Reid's words came after the Bills took a 36-33 lead with 13 seconds left in regulation. The Chiefs needed to go about 45 yards in those 13 seconds. Mahomes completed two passes, one of 19 yards to Tyreek Hill, the other for 25 yards to Travis Kelce, to set up Harrison Butker's game-tying, 49-yard field goal.

Mahomes then threw an 8-yard touchdown pass to Kelce on the first possession of overtime to win the game.

In total, Mahomes threw for 378 yards and three touchdowns, and he scored the Chiefs' first TD on an 8-yard run.

"To be in this moment in this game against that team, to make a play to walk off a game at Arrowhead, I'll remember this game for the rest of my life," Mahomes said.

"It was definitely special to win a game like this at Arrowhead. Obviously, the Super Bowl was probably number one for me, but this one is right up there. To be able to come back a couple of times, get points when we needed to get points, score touchdowns, get in field goal range, I'll remember it forever."

In the final two minutes of regulation and overtime, Mahomes was 10-of-13 for 188 yards and two touchdowns -- one the game winner to Kelce, and the other for 64 yards to Hill late in the fourth quarter.

"This is definitely another step for him into the Hall of Fame," Hill said. "He had the chance to prove once again he's at the top of the [hill] when it comes to quarterbacks in this league.

"He definitely doesn't flinch, especially in moments like that."

Mahomes' first touchdown pass of the game in the second quarter might have been his most spectacular. He was being chased in the pocket and seemingly unable to see into the end zone. But with defensive end Jerry Hughes bearing down on him, he jumped and threw into the end zone, where Byron Pringle was there to catch the 2-yard throw.