Harden, who was limited to seven appearances by a variety of right arm injuries in 2007, powered his way through the vaunted Red Sox lineup on the way to six innings of three-hit work with nine strikeouts and three walks.
"Rich showed tonight against the World [Series] champions how good he is and how much we need him," A's manager Bob Geren said. "Tonight, he pitched the way we know he can, and we're hoping to get 30-plus more of those."
The right-hander gave credit to his signal-caller for keeping him focused during his six dominant innings, during which he showed a lively fastball, splitter and changeup that had Red Sox batters out of sorts all night.
"My catcher, Kurt Suzuki, called a great game," Harden said.
"[Harden] had an overpowering fastball," Red Sox manager Terry Francona added. "When he even got in hitters' counts, he threw his offspeed, his split. He kept us off-balance. That was a very explosive game that he pitched."
With or without the assistance of his batterymate, it was apparent early that Harden wasn't fazed by the unique atmosphere around him in Tokyo Dome.
"It did feel a little different pitching in Japan," Harden said. "It felt almost like a playoff game. But you just got to treat it like any other start."
With one impressive start already in the books, Harden could match last season's total of four by mid-April.
"I've had some bad luck the last couple of years," the right-hander said. "But it was great to be out there. You've got to focus on the team and put [the injuries] behind you."
Haunted by injuries that landed him on the disabled list in each of the past three seasons, Harden didn't allow a hit until Mike Lowell's one-out single in the fourth.
Against the most potent 1-2 combination in baseball, Harden was at his best most of the night.
He held David Ortiz hitless in two at-bats, with a walk and a strikeout. Manny Ramirez struck out in the first and fourth innings.
"We had a meeting before the game with Kurt Suzuki and [pitching coach] Curt Young, talking about how we wanted to pitch them," said Harden. "Kurt Suzuki called the game. We really effectively mixed up our pitches."
The only blemish on his line came courtesy of Ramirez, who hit a two-out solo homer deep into the left-field bleachers in the sixth.
"I want to give Rich credit," Ramirez said. "He pitched a great game. He's got a nasty split, his slider was working. He's got it all."
"Manny hit a split out later on, but [Harden's] stuff was phenomenal, as was his location," Francona added.
Oakland took a 1-0 lead in the second inning on a two-out RBI single by Chris Denorfia, whose line drive to right field scored Bobby Crosby, who had doubled to open the inning.
An inning later, after Boston starter Jon Lester issued a leadoff walk to Daric Barton and surrendered a bloop single to Mike Sweeney, Brown launched his first homer in an A's uniform to left-center field.
It was sweet redemption for Brown, whose baserunning blunder between second and third in the 10th inning Tuesday cost the A's a chance at tying the game off Red Sox closer Jonathan Papelbon.
"It's a great opportunity," Brown said. "To be wanted makes you feel more comfortable when you play. It relaxes you a little bit and lets your ability come out."
The trio of Santiago Casilla, Keith Foulke and Alan Embree each threw a scoreless inning, holding the Red Sox to two hits and allowing Geren to rest closer Huston Street, who threw 1 2/3 innings in Tuesday's loss.
"We have three guys at the end of the game who have all closed games," Geren said. "One [reason] is safety. Huston did pitch [in] two innings [Tuesday] night, and it is March. And Embree and Foulke pitched well [Tuesday] night."
The A's headed home immediately after the game for their annual three-game exhibition series with the Giants, with games Friday and Sunday in San Francisco and Saturday at McAfee Coliseum.
"Nobody was looking past today," Geren said. "You have last night, which was a heartbreaker, and today you're just trying to get even."
The game was played in front of a sellout crowd of 44,735.
"The crowd was loud and the intensity was there, so it was great," Brown said. "We were all into it because the fans were into it."
"Thanks a lot to the fans," added Harden. "It's been a great experience playing here in Tokyo, and thank you to everybody."
The Red Sox and A's square off again on Tuesday in Oakland's U.S. home opener at McAfee Coliseum.
Mychael Urban is a national writer for MLB.com. MLB.com correspondent Mike Petraglia contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.