KANSAS CITY, Mo. — The Kansas City Chiefs had not even made it through two plays against Buffalo in the divisional round of the playoffs when Mike Edwards, already playing in place of injured safety Bryan Cook, clashed helmets with Bills wide receiver Stefon Diggs and had to leave their game with a concussion.

With the entire game still to go, and Bills quarterback Josh Allen on the other side, the Chiefs should have been concerned.

But in the latest example of how they’ve struck gold on Day 3 of the NFL Draft, fourth-round pick Chamarri Conner took Edwards’ place and the league’s second-ranked defense never missed a beat. Kansas City held the Bills to 24 points — the 18th time in 19 games limiting an opponent to that many or fewer — and hung on for the 27-24 victory Sunday night.

“Chamarri did a heck of a job,” Chiefs Coach Andy Reid said this week. “He’s been working in nickel and dime situations, but to come in and have that extended time in there, and make the plays he made — he sure did a nice job in there.”

The Chiefs, who now head to Baltimore on Sunday for their sixth consecutive AFC Championship Game, will always be known for their star power. They have the NFL’s reigning MVP, and arguably the face of the entire league, in quarterback Patrick Mahomes, and Travis Kelce has become just as omnipresent not only for his talent but his pop superstar girlfriend.

Throw in All-Pro defensive tackle Chris Jones and there is no shortage of big names carrying the Chiefs deep into the playoffs.

But it takes more than a handful of high-priced stars to win in the NFL. The salary cap demands it. So the teams that are able to hit on late-round draft picks and undrafted free agents, surrounding their stars with talented players on relatively paltry rookie contracts, are the ones that are best positioned to make a run at the Super Bowl.

The Chiefs quietly have done that as well as anyone.

In this past year’s draft, their Day 2 picks of Rashee Rice and Wanya Morris have been crucial to winning their eighth straight AFC West title. Rice was second among rookie wide receivers in receptions and yards receiving, giving defenses a reason to pay attention to someone other than Kelce, and Morris has appeared in 14 games on the offensive line due to injuries.

Throw in Conner and that’s quite a late-round draft haul.

It goes beyond this past year, though. In the previous draft, the Chiefs landed Joshua Williams in the fourth round and fellow cornerback Jaylen Watson and starting running back Isiah Pacheco in the seventh. Tight end Noah Gray and stalwart right guard Trey Smith were Day 3 picks in 2021, and cornerback L’Jarius Sneed and defensive end Mike Danna the year before that.

Not a bad job by Chiefs General Manager Brett Veach, who was largely responsible for picking Mahomes seven years ago.

“I’m a big Brett Veach fan,” Reid said. “I told him after the game Sunday, that’s on him. This game is him. It’s a reflection of all the time and effort his guys have put in. That’s sort of what it comes down to. They’ve given us good football players to coach.”

There is a lot that goes into making those draft steals work.

First and foremost, scouting must be on point, and the Chiefs have a group of scouts that is the envy of the league. They’ve been able to unearth overlooked talent while also identifying players that fit well in their offensive and defensive schemes.

There’s the coaching, of course, and the credentials of Reid and defensive coordinator Steve Spagnuolo can be put against anybody. And then there’s the locker room, in this case led by Mahomes and Kelce, that breeds confidence in young players that they can contribute in a significant way no matter where they played college ball or when they were drafted.

Remember, the Chiefs continually reach the AFC title game, so each draft they are picking near the end of every round.

“The great thing about Brett,” Spagnuolo said, “is that he is always communicating with us on: ‘What do you need? What fits for you? What kind of characteristics are you looking for?’ And it’s been like that from the beginning. That’s why I think he’s one of the best in the business, because the collaboration with players is terrific.”

The result of all that work is what happened Sunday night in Buffalo. Another injury to an important player could have derailed the Kansas City defense, but a fourth-round pick seamlessly stepped into a full-time role and helped them win anyway.

    Buffalo Bills running back Ty Johnson (26) carries the ball against Kansas City Chiefs cornerback Jaylen Watson (35) during the third quarter of an NFL AFC division playoff football game, Sunday, Jan. 21, 2024, in Orchard Park, N.Y. (AP Photo/Jeffrey T. Barnes)
  

    Kansas City Chiefs running back Isiah Pacheco (10) reacts after scoring a touchdown against the Buffalo Bills during the fourth quarter of an NFL AFC division playoff football game, Sunday, Jan. 21, 2024, in Orchard Park, N.Y. (AP Photo/Jeffrey T. Barnes)
  

    Kansas City Chiefs head coach Andy Reid answers questions during a news conference after defeating the Buffalo Bills in an NFL AFC division playoff football game, Sunday, Jan. 21, 2024, in Orchard Park, N.Y. (AP Photo/Adrian Kraus)
  

    Kansas City Chiefs quarterback Patrick Mahomes answers questions after defeating the Buffalo Bills in an NFL AFC division playoff football game, Sunday, Jan. 21, 2024, in Orchard Park, N.Y. (AP Photo/Adrian Kraus)