MIAMI -- Reggie Bush scored the clinching touchdown, then happily heaved the ball into the stands, and the cluster of fans scrambling for the souvenir included a man in a Miami Dolphins jersey holding a baby.
The scrum was understandable, given that victory keepsakes have been a rarity lately for Dolphins fans.
The Dolphins (2-7) ended a franchise-record streak of seven consecutive losses in Miami since last Nov. 14. They won for the second week in a row after starting 0-7.
"It was nice to come in this locker room and celebrate a win," coach Tony Sparano said. "I see 2-7 now as a hill but not a mountain. That's how our players see it, too."
The Redskins (3-6) dropped their fifth consecutive game, the longest losing streak of Mike Shanahan's career as a head coach. They haven't held a lead since Oct. 2, when they beat St. Louis.
"It's frustrating being 3-6," Grossman said. "We're better than that."
Grossman threw for 215 yards but was sacked three times and had a passer rating of 58.7, lower than his NFC-worst season figure.
Possessions by Washington reached the Miami 20, 26, 5 and 10-yard lines, but those threats produced only three field goals.
Grossman was a surprise starter, replacing John Beck four weeks after being benched. Shanahan said he decided to go with the more experienced quarterback because of a wave of injuries to the Redskins' offense.
"I thought Rex gave us a chance to win," Shanahan said. "If you have this many guys go down, I didn't want to go with the inexperienced guy and throw him to the wolves."
The Dolphins led 10-6 at halftime, then mounted scoring drives of 70 and 81 yards to seal the win. After blowing fourth-quarter leads in three earlier losses, this time they held on.
"The first seven games we were kind of in disarray," Bush said. "We were trying to find our identity. The difference now is we're playing 60 minutes and finishing at the end of games."
Miami was clinging to a 13-9 lead when Grossman drove his team 49 yards to a first down at the 10 early in the fourth quarter. He then threw a pass directly to linebacker Karlos Dansby, whose interception ended the threat.
"I have to be more careful in a crucial point in the game," Grossman said.
Vontae Davis also had an interception for the Dolphins, who doubled their season total.
After Dansby's takeaway, Miami drove 81 yards and scored the clinching TD on Bush's 18-yard run. He crossed the goal line standing up and heaved the ball into the stands in jubilation.
"We made plays that winners make at the end," Sparano said.
The Redskins' three scoring drives totaled only 48 yards. They twice took over deep in Miami territory thanks to an interception and a fumble recovery, but each time settled for a field goal by Graham Gano.
He also missed from 50 and 49 yards, and Washington netted only 61 yards rushing.
Miami's Matt Moore, the AFC offensive player of the week last week, threw an ugly interception and lost a fumble but completed 20 of 29 passes for 209 yards. The Dolphins, who came into the game last in the NFL in third-down conversions, went 8 for 14 in those situations.
They started the game in the wildcat -- the first time they've used the package this season. Running back Daniel Thomas took the snap and pitched to Moore, who threw deep and incomplete to Brandon Marshall.
Miami tried another trick play later in the drive, with Thomas throwing incomplete. More conventional was the final play of the series, a 1-yard touchdown run by Bush.
After that, Sparano went conservative. The Dolphins drew boos when they ran out the clock at the end of the first half rather than trying to score.
But nursing the early lead paid off because the Redskins couldn't cash in on their chances.
Kevin Barnes' interception in the first half gave the Redskins the ball at the Miami 5, but three plays lost 3 yards and they kicked a field goal. Washington started at the Miami 24 after Ryan Kerrigan's sack forced a fumble by Moore, and again the Redskins came away with only three points.
"You get into the red zone three times, you've got to make plays to win the game," Shanahan said.
Washington's Leonard Hankerson left the game with a strained right hip with four minutes left. He said the injury wasn't serious, but he wasn't sure whether he would be able to play in the next game. ... Redskins defensive lineman Kedric Golston left the game in the third quarter with a knee injury. ... Hankerson had eight catches for 106 yards and became the first Washington rookie since 2001 with 100 yards receiving. ... Bush rushed for 47 yards and has 242 in the past three games, a career best.
Randall Cobb, who fell hard on his right shoulder on the third play in Saturday's 39-26 preseason loss to the Eagles, avoided major injury but will have additional tests done Sunday.
The Atlanta Falcons have agreed to a five-year contract extension with wide receiver Julio Jones. Sources say he will receive $71.25 million total, with $47.5 million guaranteed.
Redskins coach Jay Gruden said he was left like everyone else -- scratching his head over how Robert Griffin III went from being cleared one day to out the next with concussion symptoms.
Baltimore Ravens wide receiver Steve Smith and Washington Redskins cornerback Chris Culliver were ejected with less than a minute left in the first quarter of Saturday night's preseason game.
There's still a possibility that the federal judge hearing the Deflategate case coaxes Giants owner John Mara or other owners into the settlement talks, sources told ESPN.
Dallas Cowboys wide receiver Dez Bryant will go into the regular season without having taken a snap in the preseason.