KANSAS CITY, Mo. -- Andy Reid doesn't want to talk about legacy and history and all that right now, which is fine. He's busy. We can do it for him.

Reid's Kansas City Chiefs won a very important football game here Saturday night. Their 31-13 victory over the Colts was the franchise's first home playoff win in 25 years -- since Joe Montana was their quarterback. It came one year and six days after the Chiefs coughed up an 18-point halftime lead and lost a home playoff game to the Titans. Saturday's win came at the expense of the same quarterback -- Andrew Luck -- who engineered a 28-point second-half comeback to beat them in a playoff game five years ago, in Reid's first season as Chiefs coach. This was a demon-exorcising victory, and Reid knew it.

"I'm into history; I love history if it makes you better," Reid said. "That was the important thing for our guys -- don't get caught up on all the stuff that happened in the past. They're out in the community. I'm not. I'm locked down in my office, so I don't hear all that stuff, but they're actually out there. So just keep it positive and move forward."

But the moving forward matters when you're talking about the Chiefs in January -- and when you're talking about Andy Reid in January. There have been too many collapses, too many near misses, too many teams that were too good to go home as early as they did, for that not to be a part of these twin stories. The Chiefs always blow it in the playoffs. Reid always blows it in the playoffs. Death, taxes and those two things.

So the fact that Reid's Chiefs won Saturday matters, because it means they host the AFC Championship Game next week. Win one home game, Andy Reid, and you go to the Super Bowl for the second time in your otherwise brilliant 20-year head-coaching career. Win one home game, Chiefs, and you go to the Super Bowl for the first time in 49 years. Decades of frigid frustration sit 60 good minutes away from erasure.

Andy Reid has led the Chiefs to their first AFC Championship Game appearance since 1993. Mark J. Rebilas/USA TODAY Sports

And this might very well be the team to do it.

"This is a new era, new team, new mindset," Chiefs defensive lineman Chris Jones insisted. "We're changing the culture around here."

They might be. Spending the week before the game in this town, I expected to find Chiefs fans gnawing their fingernails to the nubs with memories of last year, five years ago, all those playoff disappointments. But fans felt pretty good about this game, and as lifelong Chiefs fan Allen Roberson told me Wednesday night, "Mahomes is the difference."

That would be young Patrick Mahomes, the 23-year-old superstar quarterback to whom Reid turned over his playoff team a year ago without any guarantees that he could handle it. The Chiefs made last year's playoffs with Alex Smith at quarterback, and even after Smith's career year, they traded him to Washington the week of the Super Bowl, anointing Mahomes the starter after a rookie year spent sitting on the bench.

The premise of the decision made sense. The Chiefs had gone as far as they could go with Smith at quarterback. Mahomes' raw talent elevated the ceiling for them at the most important position, allowing Reid's ever-busy offensive mind to dream bigger dreams than ever. It was a risk, because young quarterbacks are always risky, but Reid knew Mahomes and believed he could be special, and he turned out to be correct. All Mahomes did this regular season was become the second quarterback in league history (after a guy named Peyton Manning) to put up 5,000 passing yards and 50 touchdown passes in the same season. The likely MVP turned out to be a weekly highlight reel of impossible deep passes, no-look passes, flying-out-of-bounds-and-whipping-the-ball-across-his-body passes. If the goal was to get the Chiefs to believe in previously inconceivable possibilities, Reid had picked the perfect quarterback to do it.

"You look last week, the rookies making their first playoff starts went 0-3," Chiefs right tackle Mitchell Schwartz said. "But none of them had 50 and 5,000 like Pat had. He's just different. Nothing bothers him."

Saturday was by no means Mahomes' most incredible game of the year. He was 27-for-41 for 278 yards, and for just the second time this year, he failed to throw a single touchdown pass. The Chiefs won this game with their run game -- piling up 180 yards on 33 carries against a tough Colts defensive front -- and their defense, which sacked Luck three times and held the league's best third-down offense to 0-for-9 on third downs.

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"Defense played lights-out all game," tight end Travis Kelce said. "And offensively, we ran the ball. When you have the lead, you'd better be able to run the ball late in the game. Damien Williams (129 yards and a touchdown on 25 carries), man, guy runs his tail off. He can finish a game off for us."

Mahomes had his highlight throws, but he didn't dominate the game the way he has so many times this year. The Chiefs found other ways to win, and don't think that's any small thing. When your quarterback allows you to dream the biggest dreams, you can absolutely be the kind of team that musters its best effort in the biggest games.

Which is why this might be the team that finally delivers for Andy Reid, who's top-10 all time in wins and might be the best non-Bill Belichick coach of his era but is 12-13 in the postseason and probably needs to win the Super Bowl at least once to ensure a spot in the Hall of Fame.

"When you play for a coach of that caliber," Williams said, "all you can do is give it your all."

Think about everything you've ever heard about Reid in the playoffs -- time management, wasting timeouts, refusing to run the ball when he has a lead. None of that came into play Saturday. Reid's Chiefs put a big lead on the board early and managed it well. Would it have been easier if they'd scored once or twice in the third quarter? Sure. But the game was never really in doubt after halftime, and that's almost never the case with an Andy Reid team in the playoffs. These Chiefs might be walking the "new mentality" walk, which could mean big things.

"We know we're part of something special," Chiefs center Mitch Morse said. "We also know the job's not done yet."

Reid has been to the conference championship game five times before, though none with the Chiefs and none since 10 years ago with the Eagles. He's 1-4 in those games, and that's another itchy part of his legacy that he'd surely love for people to stop bringing up. Next Sunday, Reid's Chiefs are going to take on a team that beat them this year -- be it the Patriots or the Chargers. It's not going to be easy, in part because nothing is easy for the Chiefs or Reid at this time of year. But this might be the year that changes. This might be the team, and the quarterback, that help stuff all that lousy history into the trash bin and put the focus on just how good a coach Reid is. You feel like Reid deserves one of these runs. And while the history tells us not to get too far ahead of ourselves, there are some pretty exciting reasons to believe this might be the team that wins it all.