MIAMI GARDENS, Fla. -- When Alex Smith threw his third touchdown pass to seal the Kansas City Chiefs' first victory, he sprinted to the end zone to join the celebration, then raised two fingers to signal his teammates to line up for a 2-point conversion attempt.
With the offense finally rolling, the Chiefs were eager to pour it on.
Smith shook off five sacks, backup Knile Davis ran for a career-high 132 yards, and the injury-plagued Chiefs earned some pain relief by beating the Miami Dolphins 34-15 on Sunday.
"Momentum's a funny thing," Smith said. "It's hard to put your finger on it, but certainly this helps. This is what you're looking for - a win on the road. A tough win, I thought. This is how you get started, for sure."
Smith led touchdown drives of 62, 76 and 66 yards in a span of four possessions as Kansas City took a 21-10 lead. The defense protected the early advantage, allowing only four third-down conversions and sacking Ryan Tannehill four times.
The Chiefs improved to 1-2 and won for only the third time in their past 11 games, including the postseason.
"I forgot how good winning feels," linebacker James-Michael Johnson tweeted.
The Dolphins fell to 1-2, another wobbly start for a team that hasn't won a playoff game since 2000.
"We have to look at everything we're doing," coach Joe Philbin said. "There was no phase where we played well enough to win."
Smith, who ranked 35th and last in the NFL in passing after two weeks, went 19 for 25 for 186 yards, with three of his incompletions dropped. Joe McKnight caught two touchdowns.
The Chiefs were without seven starters, including running back Jamaal Charles, who was inactive because of a high ankle sprain. Davis, subbing for Charles, became a workhorse with 32 carries and scored on a 21-yard run.
"I think I stepped up," Davis said. "I ran hard - made a few mistakes, but I took the workload today and I enjoyed it."
Kansas City totaled 23 first downs despite shaky pass protection. One sack of Smith resulted in a safety, and another by Jared Odrick forced a fumble that set up the Dolphins' only touchdown.
Miami's Lamar Miller gained 108 yards rushing, but poor tackling and a sputtering passing game doomed the Dolphins.
Tannehill struggled for the third game in a row, this time against a pass defense ranked as the worst in the NFL. He went 21 for 43 for 205 yards.
Many fans streamed for the exits in the final minutes, while others lingered to boo the offense.
Even when the Dolphins put up points, they could look inept. One scoring drive covered zero yards in four plays, sandwiched between rookie Jarvis Landry's 74-yard kickoff return and Caleb Sturgis' 51-yard field goal.
And after Brian Hartline caught a 1-yard touchdown pass, he celebrated by practicing his putting stroke and was flagged 15 yards for unsportsmanlike conduct.
"I just like to golf, and it just popped into my head," Hartline said. "I guess I've got to go back to dancing."
Philbin gave his many second-guessers fresh fodder. When the Dolphins ran on third-and-10 at the Chiefs 45, they gained 4 yards and had to punt. On fourth-and-2 at the Chiefs 30, they attempted a 47-yard field goal and missed it in a scoreless game.
And trailing by six points in the fourth quarter at midfield, Tannehill was sacked trying to throw on third-and-1, forcing a punt. The Dolphins were also penalized 15 yards for unsportsmanlike conduct when an official ran into a coach along the sideline.
Two plays later, Kansas City had its own gaffe, losing 15 yards on a botched exchange on a double reverse.
The Chiefs' early highlights were a pair of 64-yard punts by Dustin Colquitt. But the offense got going midway through the second quarter, mounting a 62-yard drive capped by Davis' touchdown run.
They wrapped up the victory with a touchdown after a 47-yard punt return by Frankie Hammond Jr. gave them the ball at the Dolphins 44. Smith hit McKnight to make it 27-15 with 4:35 left.
"My hat's off to the players," Chiefs coach Andy Reid said. "I'm proud of them, the effort that they gave."
Notes: McKnight's TDs were the first of his career from scrimmage. ... Dolphins LT Branden Albert was called for holding and beaten for a sack against his former team. ... Before the game, the Dolphins inducted Jeff Cross, Tony Nathan, Ed Newman and Sam Madison into their Walk of Fame.