SEATTLE — Pete Carroll flapped his arms, imploring his new home fans to get into the game. At one point, Seattle’s new coach was yanked off the field by an official after wandering too far out on the field following an enthusiastic celebration.

Eleven years after he last coached an NFL game, Carroll thoroughly enjoyed his return to pro football.

“He was probably the most enthusiastic person in the place. I got to say his energy was maybe even a little above mine and I haven’t played in that long so I was pretty excited,” Seattle linebacker Lofa Tatupu said. “Pete wants to get out there and hit.”

Matt Hasselbeck threw for two touchdowns and ran for another as the Seahawks gave their new coach a 31-6 victory over the San Francisco 49ers on Sunday.

Back on an NFL sideline for the first time since 1999, Carroll was marching up and down, almost constantly in motion. The only times he stood still was when he was giving congratulations to his players as they came off the field.

And there was plenty to give. Even more than last January when Carroll left Southern California to take over a Seattle franchise with 23 losses in two seasons, Sunday was his beginning.

“There are a ton of beginnings, but now that’s over. It’s a nice game, but it doesn’t mean that much. It’s already done,” Carroll said. “To have the opportunity emotionally to enjoy it like that in the locker room with these guys that have worked so hard that have listened to my stuff all this time, for them to feel the benefits and rewards it was very pleasing.”

While Seattle could revel in an unlikely romp to start the Carroll era in the Pacific Northwest, the 49ers were already wondering how to regroup as their lofty preseason expectations to dominate the mediocre NFC West took a major hit.

Coach Mike Singletary was instantly questioned about the future of Alex Smith as quarterback. Smith threw for 244 yards, but tossed two costly interceptions and failed to lead San Francisco to touchdowns in the first quarter when Seattle’s offense couldn’t say on the field.

“I want very much to tell Pete Carroll, ‘thank you very much for kicking our tails,’” Singletary said. “It was good medicine and we’re going to take it. We’ll go from there.”

Seattle went 1 quarters with just seven offensive plays for 11 yards, including an interception on the first play from scrimmage.

Then Hasselbeck got started. He completed 10 of his next 11 throws as Seattle abandoned an ineffective run game and used Hasselbeck’s arm. He finished 18 of 23 for 170 yards and touchdowns of 13 yards to Deon Butler and 3 yards to Deion Branch. He also bootlegged and sprinted for a 1-yard TD run in the second quarter that gave Seattle a 7-6 lead.

The ball from his touchdown run ended up in the hands of Carroll after the game, a souvenir to acknowledge his first victory with Seattle.

“Those don’t come around very often,” Hasselbeck said of the sixth rushing TD in his career and first since 2005. “Hopefully that’s the first of many for him.”

Jordan Babineaux and Marcus Trufant each intercepted Smith and Seattle’s defense held San Francisco to six points on three possessions inside the Seattle 10. Trufant returned his interception 32 yards for a touchdown early in the second half to give the Seahawks a 21-6 lead.

Smith started 9 of 10 passing, then missed 12 of his next 21 throws. The questions of how in sync San Francisco’s offense would be considering both Pro Bowl tight end Vernon Davis and receiver Michael Crabtree missed the entire unbeaten preseason, were raised again.

Crabtree looked at Smith after the pair failed to connect on two throws in the third quarter, the second returned by Trufant.

Smith finished 26 of 45 for 225 yards. Davis had eight catches for 73 yards a day after signing a five-year extension with San Francisco.

“(Mike) pointed that out. He said, ‘you can’t expect to be out then come back the first week and get the chemistry together. It takes time. It is timing, you have to trust one another,’” Davis said. “I’m not going to dwell on it. I’m going to keep encouraging the guys to keep their heads up.”

The 49ers were the trendy pick to win the NFC West, but continue to struggle winning on the road. Last year, they lost six straight road games — five in a row by a combined 19 points — before winning at St. Louis. That stretch included a 20-17 loss at Seattle in early December in which the Niners gave the game away late.

This time, there was nothing for the 49ers to give away late. Smith missed a fourth-down pass at the goal line that cost San Francisco points in the second quarter. On the next possession, a delay of game penalty at the Seattle 1 led to a field goal instead of a TD.

Frank Gore, who averaged nearly 150 yards against the Seahawks since 2006, was held to 38 yards on 17 carries and the 49ers were just 1 of 15 on third down.

“It doesn’t taste good. It doesn’t feel good,” Smith said. “I think you’ve got to try and make it a positive, but it hurts.”

Notes: 49ers receiver/returner Ted Ginn suffered a knee strain in the second half and did not return. ... San Francisco is 4-10 on the road under Singletary. ... Seattle rookie WR Golden Tate was a surprise inactive. Ben Obomanu served as Seattle’s fourth receiver and had one catch for 6 yards.