AP photo by Charlie Riedel / Kansas City Chiefs linebacker Willie Gay (50) celebrates next to the Atlanta Falcons' Luke Stocker after Younghoe Koo missed a 39-yard field-goal attempt in the final seconds of Sunday's game in Kansas City, Mo. The Chiefs won 17-14 to improve to 14-1 and clinch a first-round bye in the playoffs, while Atlanta dropped to 4-11.

KANSAS CITY, Mo. — All season, a prolific offense had been putting the Kansas City Chiefs in position to capture the No. 1 seed in the AFC playoffs and set up what they hope is a run to their second straight NFL title.

It took their defense — and some good fortune against a heavy underdog — to finally clinch it.

Patrick Mahomes threw a 25-yard touchdown pass to Demarcus Robinson with just less than two minutes to go in Sunday's game against the Atlanta Falcons, then watched the Kansas City defense force Younghoe Koo's 39-yard field-goal attempt to tie the game. When the Pro Bowl kicker faded it right with nine seconds remaining, the Chiefs had escaped, 17-14.

It was all good enough for the reigning Super Bowl champions to post a franchise-record 10th straight win and secure the AFC's lone first-round bye in this season's expanded playoffs.

"The defense played their tail off to give us a chance, and the offense found a way to score when we needed to," Mahomes said. "That's just the championship swagger to know how to win a game even when you don't play well."

Mahomes, the reigning Super Bowl MVP, was 24-of-44 pasing for 278 yards with two touchdowns and an interception as the Chiefs won their league-record seventh straight one-possession game. Travis Kelce had seven catches for 98 yards and a score, giving him 1,426 yards for the season and breaking George Kittle's record for an NFL tight end.

"The real record I'm proud of," Kelce said, "is this is the first time the Chiefs have ever been 14-1."

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AP photo by Jeff Roberson / Atlanta Falcons kicker Younghoe Koo (7) is consoled by teammate Isaiah Oliver after missing a 39-yard field-goal attempt in the final seconds of Sunday's 17-14 road loss to the Kansas City Chiefs.

The Falcons (4-11) certainly made it tougher than most people expected. They took the lead when Matt Ryan hit Laquon Treadwell for a 5-yard touchdown pass with 4:33 to go, then answered Mahomes' scoring strike to Robinson by marching right downfield again. After three straight incompletions by Ryan, though, Koo headed onto the field — and promptly missed for the first time in 36 field-goal attempts this season.

Instead of heading to overtime, the Falcons headed home with their seventh loss in a one-possession game this season.

"I told him afterwards, 'The next time you're in that situation, you're going to nail it,' and to not doubt that for a second," Ryan said. "It's part of the game and you have to move forward."

Koo, the 26-year-old from South Korea who played at Georgia Southern, made both of Atlanta's PATs to improve to 28-for-31 on those kicks.

Calvin Ridley had five catches for 130 yards for the Falcons, who were without injured veteran Julio Jones (hamstring) for the third straight game, and Hayden Hurst caught five passes for 47 yards and a score.

"They put up a great effort," Falcons interim coach Raheem Morris said of his players, "but we didn't come here to get a pat on the back by anybody. We came here to win the football game. That's the only goal you have when you come to play these games."

Both defenses played well in a first half that ended 7-7.

The Falcons' Keanu Neal picked off a pass from Sammy Watkins when the Chiefs tried an audacious fourth-down play, using the wide receiver on a reverse to throw a pass to Mahomes across the field. The pick gave Atlanta the ball at its own 2-yard line, and Ryan capped the long drive by finding Hurst on a 5-yard touchdown pass to give the Falcons the early lead.

Kansas City's offense finally got on track in the closing minutes of the first half. The Chiefs never faced third down while going 78 yards for a tying score. Mahomes zipped a short touchdown pass to Kelce, who earlier became the first tight end in NFL history and first player in franchise history with multiple 100-catch seasons when he hauled in his second reception of the game.

The stunning display of defense continued for both teams in the second half.

Falcons linebacker Foyesade Oluokun kept the game tied when he deftly stepped in front of Kelce at the goal line for an interception early in the second half. The Chiefs' defense answered by allowing just 15 yards and forcing back-to-back punts in the third quarter.

Kansas City took its first lead on Harrison Butker's 53-yard field goal with 14:08 left in the game.

The Falcons squandered their first chance to match the points when Brandon Powell coughed up the ball deep in Kansas City territory. However, they made their second opportunity count on Ryan's 5-yard flick to Treadwell that capped an eight-play, 75-yard touchdown drive late in the fourth quarter.

Then, like so many times this season, the Falcons let it slip away.

And like so many times this season, the Chiefs found a way

"I'm proud of the guys — 14-1 is nothing to shake your head at," Chiefs coach Andy Reid said. "When it's all said and done, you have a bye coming up after your next game. There's only two teams that will have that this year."