KANSAS CITY, Mo. -- Thanks in part to Alex Smith's milestone day, the Kansas City Chiefs clinched back-to-back AFC West titles for the first time in franchise history.

The Chiefs quarterback surpassed 4,000 yards passing for the first time in his 12-year career, and Kansas City rolled to a 29-13 win over the Miami Dolphins on Sunday at Arrowhead Stadium.

"I think the thing I'm more pumped about is the whole offense altogether," Smith said after topping the 300-yard mark passing in a game for the fifth time this season. "To have a 1,000-yard rusher, two 1,000-yard receivers and then to hit 4,000 passing as a quarterback, to have all that going on at once I think is the most special part."

Smith delivered again in the best season of his career, completing 25 of 39 passes for 304 yards and a touchdown.

Wide receiver Tyreek Hill led the Chiefs with six catches for 109 yards. Running back Kareem Hunt added 91 rushing yards on 29 carries with a touchdown, and Harrison Butker converted five of six field-goal attempts.

Kansas City (9-6) took its first lead thanks to a Dolphins turnover on their first drive of the game. Linebacker Derrick Johnson jarred the ball loose from wide receiver Jarvis Landry after a short gain, and cornerback Marcus Peters grabbed it along the sideline. That set up the Chiefs with a short field, and Butker hit a 31-yard field goal to put Kansas City up 3-0.

After the Dolphins (6-9) tied the game with a 44-yard field from Cody Parkey, Smith gave the Chiefs a lead they would not relinquish. Smith found Hill on a third-and-15 pass deep down the middle for a 52-yard gain. That set up a 9-yard touchdown pass from Smith to tight end Travis Kelce for a 10-3 lead.

"We're just playing confident football," Kelce said of the team's offensive performance. "Confident that guys are going to make plays when the ball's in the air, that Alex is going to put that thing right on the money where it needs to be and that the guys up front are going to give him time."

Dolphins coach Adam Gase said, "We got beat by a couple of guys we talked about stopping. That's really what hurt us."

Quarterback Jay Cutler kept Miami in the game in the first half. One play after the Chiefs extended their lead to 17-6 with a 1-yard touchdown run from Hunt, Cutler connected with wide receiver Jakeem Grant on a short pass, and Grant did the rest. He darted 65 yards through the Kansas City defense for a touchdown, pulling Miami within 17-13.

Smith, however, hooked up with Hill for another big gain late in the first half to set up another Chiefs scoring drive. Smith lofted a ball down the right sideline for Hill, who made a quick adjustment out leaping Dolphins safety T.J. McDonald for a 33-yard gain. Butker added a 32-yard field goal making it a 20-13 game at the half.

The Kansas City defense came through in the second half by shutting out the Dolphins. Despite a hot first half with 169 passing yards, Cutler wound up completing 19 of 38 passes for 286 yards and a touchdown.

"He was good," Gase said of his quarterback. "There's a couple of things I'm sure when he goes back and looks at this he'll probably want back. But I thought for the most part he did a really good job, he controlled the game as much as he could. But in the second half, we just really didn't do much."

Cutler said settling for field goals early and making mistakes in the second half took their toll.

"The offense was really rolling pretty good at times, and I thought we moved the ball really well," Cutler said. "I think there's only one drive we had that three-and-out. Other than that, a couple of fumbles, a couple of missed opportunities here, a penalty when we were driving. Those type of things hurt you in a big way."

Chiefs coach Andy Reid gave credit to defensive coordinator Bob Sutton for his defense holding the Dolphins without a conversion on eight third-down plays during the game.

"For a team like that not to have converted on third down, that's something special," Reid said.

Grant caught four passes for 107 yards and a touchdown to lead the Dolphins. Kenyan Drake added 57 yards on 13 carries.

Butker completed Kansas City's scoring with a 49-yard field goal, banking it off the left upright late in the fourth quarter. That gives him 36 field goals on the season, eclipsing the franchise record of 34 set by Nick Lowery in 1990.

NOTES: The Chiefs forced two turnovers against the Dolphins, giving their defense nine takeaways in the past three games. ... Dolphins WR Jakeem Grant's 107-yard receiving day was a career high. He entered the game with just 178 yards receiving on the season. ... Kansas City's Travis Kelce went over the 1,000-yard mark receiving on the year, joining Hall of Famer Tony Gonzalez as the only tight ends in franchise history with multiple 1,000-yard receiving seasons. ... Dolphins S Reshad Jones led both teams with 15 total tackles in the game. ... With QB Alex Smith topping 4,000 passing yards, Kelce joining WR Tyreek Hill in the 1,000-yard receiving club and RB Kareem Hunt earlier hitting the 1,000-yard rushing mark, the Chiefs joined the 1981 San Diego Chargers as the only teams in NFL history with a 4,000-yard quarterback along with 1,000-yard running back, tight end and wide receiver in the same season.