They did it again on Sunday, holding on down the stretch for a 23-17 win over the Browns.
"Everything he's been through, it's contagious," Chiefs safety Eric Berry said. "We soak it up like sponges and use it throughout games, and not just in games, but in life."
The Chiefs got off to a quick start and led 20-7 shortly before halftime, but the Browns came storming back behind quarterback Jason Campbell. He wound up throwing for 293 yards and a pair of touchdowns in place of the ineffective Brandon Weeden, and had his team within a field goal with the ball in the closing minutes of the game.
That's when the Chiefs (8-0) stood tall on defense.
They forced Campbell out of the pocket, and his throw across the field hit Davone Bess in the hands and bounced to the turf for an incompletion. Ryan Succop tacked on his third field goal of the game, and the Chiefs had another narrow win locked up.
"Every win is a good win," Reid said, "but this one was a little close."
If nothing else, Campbell may have solidified the starting job for the Browns (3-5). Weeden took over when Brian Hoyer went down with a season-ending injury, but struggled so much in a loss to Green Bay last week that Campbell was given the nod on Sunday.
He performed well against one of the NFL's top defenses, too. He didn't turn the ball over while eluded just about every blitz that Kansas City's aggressive defensive ends tried to bring.
"He made some big plays for us," Browns coach Rob Chudzinski said. "I think his leadership was key in us being able to hang in there and keep fighting after the early deficit."
Here are five other keys to the game:
GORDON GONE? Josh Gordon had a big game in what may be his final appearance for the Browns, catching five passes for 132 yards and a touchdown. The Browns have been fielding offers for the wide receiver ahead of Tuesday's trade deadline. "I do definitely want to stay in Cleveland. Cleveland is my first home, the team I was drafted to," he said. "It's a great place to be and play for. I love the fans in Cleveland and everything about it. But business is business."
CHARLES ACHING: Chiefs running back Jamaal Charles had 120 yards of total offense, but left the game briefly to get treatment on a bruised knee. He still finished out the game. "I'm happy that I finished," he said. "It's a long season and I'll get banged up every week."
CAMERON CONTAINED: The Browns' Jordan Cameron came into the game leading NFL tight ends in catches (45) and was second in yards (515) and touchdowns (six). He also was going against a defense in Kansas City that has struggled to contain tight ends. Cameron wound up with four catches for 81 yards, but most of that came on a 37-yard reception.
HIT THE ROAD: The Chiefs have won their last three games in the friendly environs of Arrowhead Stadium, where the home crowd set a Guinness world record for loudest outdoor sports venue a couple of weeks ago. Now, they'll have to head back on the road to play Buffalo before getting a week off. "Being at home these three weeks in a row helps because we're able to get a little extra rest," Reid said. "Those grind-it-out ones are especially tough."
TALE OF TWO HALVES: The Browns struggled to get going in the first half, and had just 18 yards of offense before Campbell led them on a TD drive late in the first half. But once they got into the game, Cleveland made it competitive. "We've just got to start fast," linebacker Craig Robertson said. "We started slow in the first half and picked it up in the second, but we've got to play four quarters to win in this league."
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