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CINCINNATI -- One game into their weeklong trip, the San Francisco 49ers already have a very nice gift to take home and put on the shelf.

And they've left room in the suitcase for one more.

Kendall Hunter ran 7 yards for the game's only touchdown with 3:59 to go Sunday, rallying the 49ers to a 13-8 victory over the Cincinnati Bengals that began their extended stay in the Buckeye State on an upbeat note.

The 49ers (2-1) haven't had many wins on East Coast time lately, and it looked like they'd forgotten to pack their West Coast offense. San Francisco didn't even cross midfield for the first time until midway through the third quarter.

Trailing 6-3, the 49ers put together their only drive of the game for the winning score, stunning the smallest crowd for a Bengals home opener in 30 years.

Now, there's something to write home about.

"To become that type of team that wins on the road and take that next step, you have to win like this," said Alex Smith, who was 4 of 5 for 48 yards on the winning drive. "I think guys were frustrated, but in a good way. They were frustrated and fired up. They wanted the ball back.

"That was different. A lot of times, I've been on teams where it's kind of, 'Here we go again,' and this is a lot different."

It was a satisfying start to the 49ers' visit to Ohio. They'll practice at Youngstown State the next few days, then head to Philadelphia for their next game.

What do they think so far?

"It's a lot different over here," Hunter said.

Sure is. In a lot of ways.

There were only 43,363 fans at 65,500-seat Paul Brown Stadium, the Bengals' smallest crowd for a home opener since they played at Riverfront Stadium in 1981. Cincinnati (1-2) was limited to a pair of field goals by Mike Nugent during rookie quarterback Andy Dalton's first dismal performance. He threw two interceptions in the fourth quarter, the first of his career.

The 49ers sent that small crowd heading for the exits when Reggie Smith intercepted Dalton's throw with 1:45 left.

"We started fast, which is what you come out to do," said Dalton, who led the Bengals to an opening field goal. "We were flat after that. We couldn't do the things we wanted to do."

David Akers kicked three field goals for San Francisco, including a 53-yarder after Dalton's first interception, pushing the lead to 13-6. After Smith intercepted Dalton again with 1:45 to go, punter Andy Lee ran out of the end zone for a safety to finish it with 2 seconds left.

Those last few minutes by the 49ers decided an ugly game overall: 12 punts, two field goals combined through three quarters.

"It hasn't been like this in here for a long time," cornerback Shawntae Spencer said. "On the road, you want to keep it close and try to steal it late."

The late drive did it.

Smith was under constant pressure and finished 20 of 30 overall for 201 yards and five sacks. The 49ers blunted drives with penalties, and Kevin Huber's punts pinned them at their 10, 11, 12, 14 and 17, leaving too much ground for one of the NFL's least-productive offenses to cover.

Also, the 49ers were missing receiver Braylon Edwards, who hurt his right knee during an overtime loss to Dallas last Sunday.

The 49ers pulled a play from deep in their book to set up the go-ahead touchdown. Smith faked a handoff and rolled to his right, then turned and threw back to his left, where tight end Vernon Davis was open for a 20-yard catch-and-run that put San Francisco in position to win it.

"I had the call on and I saw they were bringing pressure, so I really tried to sell the fake," Smith said. "He made a great play with the ball in his hands."

The Bengals were at full strength after deciding to let receiver Jerome Simpson play. He missed two days of practice because he's the focus of an investigation into a drug shipment to his home. He got into the game on the opening series and finished with one catch for 6 yards.

Coach Marvin Lewis decided a couple hours before the game to let Simpson play.

Dalton had passer ratings above 100 in his first two starts, but repeatedly forced throws against the 49ers' defense. He went 17 of 32 for 157 yards and a rating of 40.8.

Game notes

Bengals RB Cedric Benson carried 17 times for 64 yards, extending the 49ers' streak of stopping the run. They came in with the league's top run defense, allowing 54.5 yards per game. They haven't allowed a 100-yard rusher in the last 25 games. ... Akers made field goals of 23 and 53 yards, giving him 301 in his career. ... San Francisco has an 11-3 edge in the series, including two Super Bowl wins. ... The smallest crowd in Paul Brown Stadium's 12-year history was 42,092 for a 29-15 loss to Jacksonville on Dec. 15, 2002. The Bengals went 2-14 that season. ... The Bengals are 2 of 21 on third downs in the last two games.