The quarterback of the Kansas City Chiefs, Patrick Mahomes, has accomplished more than most during his seven seasons in the National Football League. He has won two Super Bowls and twice earned the league’s Most Valuable Player award. 

One thing that Mr. Mahomes hasn’t done, though, is win a playoff game on an opponent’s field, something that could change on Sunday when the Chiefs visit the Buffalo Bills in the Divisional Round of the American Football Conference.

Mr. Mahomes is 12-3 in the playoffs comprising those two Super Bowl victories. Through each of those runs, the Chiefs held home-field advantage and never had to venture away from Arrowhead Stadium. This year Mr. Mahomes will be without the support of the Chiefs’ home crowd and will need to defeat the Bills at Buffalo — a tall order —  to advance to the AFC Championship.

“Obviously, I’ve been lucky enough to play a lot of games at home at Arrowhead Stadium,” Mr. Mahomes told reporters at Kansas City. “Everything has fallen that way. Now we have a great opportunity to go on the road and play in a hostile environment, one I haven’t been able to play with fans in the stands. Even though I know it’s going to be hostile and people talking trash, I’m excited for it. It’s one of the best environments in football.”

It will be cold and loud at Highmark Stadium at Orchard Park, where the notorious Bills Mafia awaits a team that eliminated them from the playoffs following the 2020 and 2021 regular seasons. More recently, Buffalo defeated the Chiefs 20-17 at Kansas City in December to earn home-field advantage. The Bills, champions of the AFC East, advanced to the Divisional Round with an emphatic 31-17 triumph over the Pittsburgh Steelers in the Wild-Card Round. The Chiefs defeated the Miami Dolphins, 26-7.

The Divisional Round begins Saturday with the Houston Texans at the top-seed Baltimore Ravens at 4:30 p.m. and the Green Bay Packers visiting the San Francisco 49ers at 8:15 p.m. The opening game on Sunday has the Tampa Bay Bucs at the Detroit Lions at 3 p.m. The Chiefs and Bills collide at 6:30 p.m. Winners advance to Championship Sunday next weekend.

The Bills were 7-2 at home this year and have won six straight games. They played one of their most complete games of the season in beating the Steelers. Quarterback Josh Allen enjoyed a brilliant outing, passing for three touchdowns and running for another to lead the Bills to an emphatic win in a game delayed by a snowstorm.

“To think about how far we’ve come even from seven, eight weeks ago to where we are now to have an opportunity to host a game against a team that has won two championships in the last couple of years, you can’t help but be excited for that,” Mr. Allen said at Buffalo.

The matchup between Messrs. Mahomes and Allen is the headliner, a confrontation of two of the best and most daring quarterbacks in the NFL. They are 3-3 in games against each other, but Mr. Mahomes has all the hardware. In addition to his two league MVP awards, he is a two-time Super Bowl MVP.  Mr. Allen, meanwhile, is trying to get back to the AFC Championship game. The last time he was on that stage, in 2020, he lost to Mr. Mahones and the Chiefs. 

“He’s not an easy match-up for any team,” Mr. Allen said. “They’ve gotten the best of us in the playoffs in the last few years. We’ve finally got a home game. We’ve just got to put our best foot forward and play as hard as we can play.”

Both teams endured their share of adversity during the season. The Bills were 6-6 after a 37-34 overtime loss to the Philadelphia Eagles. Fans were questioning Mr. Allen and head coach Sean McDermott. But the win over the Chiefs and a change to Joe Brady from Ken Dorsey as the offensive coordinator launched a six-game winning streak.

“I’m feeling good about how well we’re playing as a unit in terms of communication, energy, and attention to detail,” Mr. Allen said.

Meanwhile, the Chiefs finished 5-5 over the last 10 regular-season games, even with the ardent support of pop star Taylor Swift.  The emergence of running back Isiah Pacheco and wide receiver Rashee Rice has jump-started a Chiefs offense that has appeared rickety this season and prone to back-breaking drops.  

“We understand that it’s going to be a great challenge,” Mr. Mahomes said. “We understand it’s going to be a hostile environment and we’re playing a great football team that has won [six] games in a row. It’s not always going to be high flying, but we’re going to do whatever we can to win the football game.”