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KANSAS CITY, Mo. -- It didn't matter how big of a lead the Miami Dolphins built on the Kansas City Chiefs. It still wasn't enough to keep them from feeling jittery.

One of two winless teams left in the NFL, the Dolphins came into Arrowhead Stadium on Sunday with the cloud of two second-half collapses still hovering. They were also facing a Chiefs team that had mastered the art of the comeback: 0-3 to 4-3 in four games.

So it made sense that nobody on the Dolphins sideline was celebrating until the final seconds ticked away, and coach Tony Sparano's beleaguered team could finally enjoy a 31-3 victory.

"I'm just happy for the guys in our locker room," Sparano said. "All I've wanted to do for seven weeks is see these guys smile."

There was plenty to smile about.

Matt Moore threw for 244 yards and three touchdowns, the first three-TD performance by a Miami quarterback since Chad Pennington in 2008. Reggie Bush ran for 92 yards and another score, and tight end Anthony Fasano hauled in two touchdown passes in the first half.

Brandon Marshall finished with eight catches for 106 yards and another score, once again making for a miserable afternoon for the Chiefs. The former Broncos wide receiver has 52 catches for 689 yards and seven touchdowns in eight games against Kansas City in his career.

"We had a couple of big plays, which kind of lit the fire," Moore said. "You make a couple of big plays early and there's no telling what can happen."

The virtuoso performance by the Miami offense helped brush away the spectre of an 0-7 start, which included a pair of disheartening losses the past two weeks: The Dolphins blew a 15-point lead in an overtime loss to Denver and a seven-point lead last week against the New York Giants.

"This is all about the players," Sparano said. "These guys did a super job all week long of putting all the garbage behind them."

Kansas City, meanwhile, looked more like the team that lost its first two games by a combined 89-10 than the one that rattled off four straight wins to climb into a tie atop the AFC West. The Chiefs, Chargers and Raiders remained tied for first place in the division after all three lost Sunday.

Matt Cassel was 20 of 39 for 253 yards despite facing a secondary missing cornerback Vontae Davis and had backup Nolan Carroll leave several times with a hamstring injury.

Of course, the defensive backfield didn't have much to defend.

The Dolphins' relentless front spent most of the afternoon in Cassel's face, sacking him five times and forcing the slow-footed quarterback to scramble nine more times. The Chiefs came into the game having allowed 13 sacks all season, tied for sixth-best in the league.

"They executed and we didn't," Cassel said. "We were able to put together some drives, but we weren't able to sustain those drives offensively. We have to do a better job of executing. It starts with me and all the way down the line."

Things looked promising for Kansas City its opening possession, when it put together a grinding, 14-play, 53-yard drive that Ryan Succop finished off with a 43-yard field goal.

The Chiefs didn't do much after that.

Miami answered with a touchdown later in the first quarter when nobody pick up Fasano off the line of scrimmage. Moore simply tossed a pass to him from 3 yards out, the first of 31 straight points scored by the Dolphins -- more than they'd scored in any game this season.

On the Dolphins' ensuing possession, Moore hit fullback Charles Clay for gains of 21 and 22 yards, and then found Fasano open down the sideline for a 35-yard touchdown completion and a 14-3 lead.

Fasano's only other two-TD game also came against the Chiefs.

The Dolphins offense really hit the accelerator in the third quarter, when Moore found Marshall for a 14-yard touchdown pass, and Bush shook loose for a 28-yard scoring run, the former No. 2 overall draft pick's first TD on the ground since Nov. 15, 2009.

Any chance of a comeback ended early in the fourth quarter, when Kansas City failed to convert on fourth down at the Dolphins 3. The Chiefs also couldn't score on fourth-and-goal at the 5-yard line in the closing minutes of the game.

"This was not the kind of performance we expected or wanted," Chiefs coach Todd Haley said stoically. "This was a very dangerous team that was playing a lot better than their record. It's hard to win in the NFL and they just did a better job than us."

Chiefs cornerback Brandon Flowers put it more succinctly.

"We got beat," he said. "We got beat pretty bad by the Miami Dolphins. At home."

Game notes

LB Jason Taylor played in his 196th game for Miami, tied with OL Bob Kuechenberg for second place on the franchise list. ... The three points allowed by the Dolphins were the fewest since they beat Buffalo 16-3 on Dec. 7, 2008. ... Jackie Battle carried 14 times for 40 yards for the Chiefs. Cassel was their second-leading rushing with nine carries for 38 yards. ... The Chiefs have lost eight of their last 10 games against Miami.