Kansas City, Mo. — Alex Smith has earned plenty of detractors over the course of his career, getting labeled as a "game manager" and a quarterback who is unable to lead his team when the pressure is on.

He quieted all those doubters once again Monday night.

Smith threw for 293 yards with touchdowns through the air and one on the ground. His 37-yard pass to Albert Wilson on a broken play late in the fourth quarter set up Harrison Butker's go-ahead, 43-yard field goal that helped push Kansas City to a 29-20 victory over the Washington Redskins.

"Alex never says anything. Everybody else says everything," Chiefs coach Andy Reid said. "He just keeps doing good and doesn't worry about all that. He's a seasoned veteran.

"I've told you before, I love the guy," Reid continued. "He's everything you want as a coach and comes to work every day. He's the first one in and the last one out. All of these things that you're supposed to do, he does. This is what we see every day."

He certainly outplayed his more touted counterpart, Redskins quarterback Kirk Cousins (Michigan State), who threw for 220 yards and two touchdowns but was unable to march his team for a touchdown down the stretch.

They had to resort to a 40-yard field goal with 47 seconds left, enough time for Smith to lead the Chiefs the other way and get Butker into position for his go-ahead kick.

Justin Houston returned a fumble for a touchdown on the final play of the game.

"It was a great game. Both teams were fighting, playing hard," Redskins linebacker Mason Foster said. "We've got to make more plays so we win. That's what it comes down to."

Both teams had key contributors fall victim to injuries during this game. Chiefs right guard Laurent Duvernay-Tardif went down with a knee injury in the first quarter, and was quickly deemed out. After the game, Reid said that Duvernay-Tardif sprained his knee.

"We'll do all the tests tomorrow and see exactly where he's at there," Reid said.

Redskins cornerback Josh Norman fractured a rib, and coach Jay Gruden expects him to miss a few weeks. Their secondary would continue to be depleted, as a number of other defensive backs — including starting safety Deshazor Everett, who hurt his hamstring — would go down for at least part of the game.

Running back Rob Kelley left with an ankle sprain and offensive tackle Trent Williams missed time as well, meaning the Redskin's bye next week comes at the perfect time.

Chiefs running back Kareem Hunt continued his strong rookie campaign, rushing for 101 yards on 21 attempts. But despite joining Curtis McClinton for the second-most 100-yard rushing games in a Chiefs' rookie season, all that matters to him is that Kansas City is unbeaten.

"Winning is more meaningful," Hunt said. "I could have 50 yards, as long as we win, I'm happy."

Reid is happy to see that approach in his budding star.

"He's keeping a level head about it which is important," Reid said. "He's a young guy and he's getting a lot of accolades, and he got a ton of them last week, and came out and played hard-nosed."