David DeJesus got Oakland on the board with a first-inning RBI groundout, then Hideki Matsui added a two-run double and Daric Barton and Kurt Suzuki each hit RBI singles in a four-run eighth. Anderson (1-1) allowed four hits and walked one in eight innings, helping the A's (9-8) move over .500 for first time this year.
The Red Sox were coming off a 9-1 win over the Blue Jays, highlighted by 13 hits and three home runs. Boston remains winless away from Fenway Park and was blanked for the second time this season after losing 1-0 at Cleveland on April 7.
Red Sox manager Terry Francona was ejected for the first time this year for arguing a play on the basepaths in the fourth.
Anderson looked sharp all night and improved to 4-1 with a 2.08 ERA in six career starts against the Red Sox. A's starters have allowed just one earned run over their last five games — spanning 33 2/3 innings — for a 0.29 ERA.
Boston had a chance against Anderson in the eighth after David Ortiz led off with a single and was lifted for pinch-runner Jacoby Ellsbury. But Mike Cameron struck out and was called for interference as Ellsbury tried to steal second, making for a double play.
Anderson then allowed back-to-back singles to Carl Crawford and Jarrod Saltalamacchia before striking out Darnell McDonald.
Craig Breslow and Brian Fuentes combined to finish the five-hitter.
In the seventh, Anderson tripped on the front of the mound and committed Oakland's majors-leading 19th error while making a throw to first after fielding Adrian Gonzalez's comebacker. But Anderson got Kevin Youkilis to ground into an inning-ending double play.
After Gonzalez's two-out single in the first, Anderson didn't allow another hit until Ortiz's single. The burly left-hander retired 16 of 17 Boston batters during one stretch with only a leadoff walk to Dustin Pedroia in the fourth.
Pedroia was caught stealing moments later and Francona was ejected by plate umpire Jim Reynolds for arguing.
Lackey (1-2) allowed four hits in six innings, struck out three and walked one in his best start so far. The right-hander threw two side sessions under the guidance of first-year Red Sox pitching coach Curt Young during a long layoff between starts. He was supposed to pitch last Wednesday but the game against Tampa Bay was rained out.
Lackey — 17-6 with a 2.86 ERA against the A's in 32 career starts, most of those coming during his days with the AL West rival Angels — lowered his ERA from 15.58 ERA to 9.82 after struggling through his first two outings of 2011.
But Boston couldn't generate much offense in the opener of a quick, two-game visit to the Coliseum — one of only two West Coast trips for the Red Sox this season. They came to Oakland twice in 2010 and also played in San Francisco for interleague. The A's go to Fenway Park for a pair of three-game series.
After this stop, the Red Sox head to Southern California to play four games with the Los Angeles Angels before three games at Baltimore. They don't come back West until August at Seattle.
Boston fell to 0-7 on the road.
Francona stuck with the hot hand of shortstop Jed Lowrie, who entered batting .516 with two home runs and nine RBIs. Lowrie went 0 for 4 with two strikeouts and had his seven-game hitting streak snapped. Francona said he is communicating with Marco Scutaro and is writing the lineup based on performance.
Notes
Francona was ejected for the 30th time as a manager. … A's LHP Dallas Braden, placed on the 15-day disabled list Monday with a shoulder injury that forced him out of his Saturday start early, is scheduled to be examined by renowned orthopedist Dr. Lewis Yocum on Wednesday in Los Angeles. RHP Tyson Ross will start in Braden's spot Friday at Seattle. … Oakland RHP reliever Michael Wuertz (strained left hamstring) is set to pitch in a rehab outing for Triple-A Sacramento at Reno on Wednesday — going four or five outs. … Young returned to Oakland for the first time since spending the past seven seasons coaching the A's pitchers.