KANSAS CITY, Mo. -- A placekicker making his NFL debut ensured that the Kansas City Chiefs would remain the league's lone unbeaten team.

Harrison Butker's third field goal of the game, a 43-yarder with four seconds remaining, lifted Kansas City to a 29-20 win over the Washington Redskins on Monday night.

"I knew it was going to come down to a field goal," Butker said about his nerves before the game-winning kick. "I felt pretty calm. I was excited, I wasn't nervous, I didn't have butterflies, and I hit the ball well."

Butker's late field goal broke a 20-20 tie. Linebacker Justin Houston returned a fumble for a 13-yard touchdown on the last play of the game to account for the final margin.

Butker tied the game at 17-17 with a 26-yard field goal in the final seconds of the third quarter, and his 32-yarder with 4:55 left in the fourth quarter put the Chiefs ahead 20-17.

The rookie missed his first kick of the game wide left. The 46-yard try would have tied the game with six seconds remaining in the first half. Kansas City head coach Andy Reid said he didn't worry about his new kicker with the game on the line.

"I was confident because he was confident," Reid said. "I talked to him after the first miss, and he goes, 'I got it, I got it, I was off by a tad.' He kind of gives you that feeling that everything is OK."

Butker signed with the Chiefs last week after kicker Cairo Santos sustained a groin injury in the previous game. Santos subsequently was released from injured reserve on Saturday.

Washington head coach Jay Gruden thought his team scored a go-ahead, 22-yard touchdown with just less than a minute remaining in the game. Quarterback Kirk Cousins had tight end Jordan Reed on a double move, but instead he threw to wide receiver Josh Doctson in the end zone.

Doctson initially appeared to make the catch before he hit the ground, and the ball squirted free with Chiefs cornerback Phillip Gaines tumbling to the turf with him.

"Josh almost had it," Gruden said. "He made an unbelievable effort for the ball, unfortunately couldn't hold it in with hitting the ground."

Washington settled for a field goal, with Dustin Hopkins tying the game at 20 by making a 40-yarder with 47 seconds remaining.

Quarterback Alex Smith then marched the Chiefs 50 yards in six plays for the winning score.

Smith teamed with wide receiver Albert Wilson on the key play of the drive. Smith evaded pressure in the pocket, scrambling to his right and finding Wilson downfield for a 34-yard gain to the Washington 37-yard line.

"I knew we had a couple of timeouts, so just trying to see if you get a chunk here or there," Smith said. "Luckily we were able to get it there on the second play with the scramble. Albert made a heck of a play reading that and then the catch."

Rookie Kareem Hunt powered Kansas City (4-0) during its comeback from a 10-7 halftime deficit. The NFL's leading rusher collected 101 yards on 21 carries, with 78 yards coming in the second half.

"I feel like we do a great job of wearing them down," Hunt said about his second-half success. "The 2-, 3-yard gains, sometimes we try to make them feel it a little bit. We just keep battling and going back at it. Everybody's on the same page, and we just got to finish."

Smith gave the Chiefs their first lead of the game midway through the third quarter with a 1-yard touchdown run.

The Redskins (2-2) had one last chance to win the game on the final play. However, Washington fumbled on a quick succession of laterals, Houston recovered the loose ball and went in for the score.

Smith completed 27 of 37 passes for 293 yards and one touchdown. Cousins was 14 of 24 for 215 yards and two scores, and he also led his team with 38 rushing yards.

"When teams play man coverage, that's when you really have an opportunity to run because guys are chasing their man and they don't have eyes on you," Cousins said. "They did a good job of taking guys away and doubling some people, and really all I had was to run, and that's an area of my game that I can use more, I think."

The Chiefs experienced a key injury on their first offensive series, losing starting right guard Laurent Duvernay-Tardif for the game with a left knee injury. Jordan Devey took over at right guard in his absence. Left tackle Eric Fisher, a game-time decision due to back spasms, was in the starting lineup. The Chiefs also were without starting center Mitch Morse, who sustained a foot sprain in Week 2.

Center Zach Fulton, filling in for Morse, said the offensive line didn't discuss any major in-game changes, but rather focused on playing to its own strengths and continuing with the game plan.

"We struggled the first drive to begin with," Fulton said. "Sometimes that's how the game goes. You can't let anything get you down. You've got to keep going."

Washington sustained losses on both sides of the ball. Star cornerback Josh Norman injured his ribs in the second quarter and was ruled out for the game.

Gruden told ESPN sideline reporter Lisa Salters at halftime that he expected Norman to be out a "couple of weeks." Norman left the game shortly after delivering a big hit on tight end Travis Kelce (seven catches, 111 yards, one touchdown).

Washington running back Rob Kelley exited the game in the second quarter with an ankle injury. A few plays later, Redskins left tackle Trent Williams left the game with a right knee injury, but he later returned. Gruden felt the injuries took their toll on the team's offense.

NOTES: Washington TE Vernon Davis had the game's longest reception, 69 yards. He finished with two catches for 89 yards. ... Four Redskins recorded one sack apiece, while the Chiefs never sacked Washington QB Kirk Cousins. ... Kansas City has a 26-4 record in its past 30 regular-season games. ... The Redskins ended the Chiefs' NFL-record, nine-game streak of recording a touchdown play of more than 50 yards. ... The Chiefs play the Texans in Houston on Sunday. ... Washington is headed into its bye week before a return to action Oct. 15 at home against the San Francisco 49ers.