KANSAS CITY, Mo. -- If the Kansas City Chiefs could have designed the way they will enter the AFC Championship Game, they would have drawn up their 31-13 divisional-round win against the Indianapolis Colts.

The Chiefs didn't merely beat the Colts on Saturday, they used them as a launching pad. Kansas City will have a full head of steam going into next week's game against the winner of the Los Angeles Chargers and New England Patriots (1:05 p.m. ET, Sunday). The AFC title game will be in Kansas City for the first time.

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"It's been a long time coming," Chiefs chairman Clark Hunt said. "It's something we feel as an organization we should have accomplished in recent history. Since Andy [Reid] came here, we've had a lot of shots. But finally we get a chance to win that AFC championship and to get to do it at home is so special for us."

The victory was a big confidence boost for the Chiefs, particularly on defense. They played their best defensive game of the season, forcing the Colts to go three plays and punt on each of their first four possessions.

The defense pitched a shutout until the Colts scored an offensive touchdown with less than six minutes left. The Colts scored their first touchdown on a blocked punt in the second quarter.

The Chiefs, who entered the game allowing 18 points a game at home, didn't allow a touchdown in their final regular-season game, a 35-3 win against the Oakland Raiders.

Kansas City made some recent defensive lineup changes that seem to be working. Third cornerback Charvarius Ward and safety Jordan Lucas, who is starting in place of the injured Eric Berry, have played well over the past couple of games.

The Chiefs had been plagued by defensive penalties most of the season but against the Colts they had just one -- a pass interference call against Ward with 41 seconds remaining. They had no defensive penalties against the Raiders.

"You could feel the energy all week," Reid said. "I think some of the young guys are maturing right in front of our eyes and playing well. We added a couple of guys in there. ... Everybody's taking up their game."

With the emphatic victory, the Chiefs buried their many playoff demons. They won at Arrowhead Stadium in the playoffs for the first time since January 1994. The streak included losses of one, two, three and four points.

The Chiefs had lost 11 of their previous 12 playoff games, with four of those defeats coming against the Colts.

They won't have that ugly history hanging over them heading into the AFC title game. They buried it early by rushing to a 17-0 lead in the second quarter.

Patrick Mahomes completed 27 of 41 passes for 278 yards against the Colts. Jay Biggerstaff/USA TODAY Sports

"It is great to get that talking point behind us," Hunt said. "There was a lot of noise obviously out there about it. The fans had a lot of anxiety about it. That's all now in the rearview mirror."

Against the Colts, the Chiefs had to survive some anxious moments having more to do with their playoff history -- they wasted a 28-point, third-quarter lead against the Colts five years ago and an 18-point, third-quarter lead against the Titans last season -- than the way they were playing.

But they finished strong this time. A Sammy Watkins fumble at the Kansas City 20 gave the Colts some apparent life late in the third quarter.

But Dee Ford forced Andrew Luck to fumble two plays later. The Chiefs recovered and were never again seriously threatened.

Every time the Colts did something positive -- their blocked punt, the Watkins fumble and their fourth-quarter touchdown -- the Chiefs answered. They scored a touchdown of their own after each of the Indianapolis TDs.

That kind of resilience had been in short supply for the Chiefs in the playoffs. When things started to go bad, they went bad in a big way.

But with some help from their defense, the Chiefs changed their postseason narrative, perhaps for good.

"All the way around, everybody contributed," Reid said. "It's important this time of year that you do that."