But in order to do so, they'll have to get by Jon Lester, who nearly no-hit them last month.
Oakland seeks its sixth straight win and eighth in nine games Sunday against Lester and Boston.
The Athletics (47-28) improved upon their major league-leading record Saturday, beating Boston for the 21st time in 26 meetings in Oakland with a 2-1 victory in 10 innings. Coco Crisp drove in Alberto Callaspo with a single on Koji Uehara's first pitch and is batting .356 with nine RBIs over his last 12 games.
Despite their recent dominance against the Red Sox, the Athletics haven't taken a four-game home series from them since May 19-21, 1932, when they were based in Philadelphia. They won four straight at Boston from Aug. 10-12, 1971.
Lester (8-7, 3.20 ERA) proved more than capable of shutting down Oakland on May 3, striking out a career-high 15 while yielding just one hit and two walks over eight innings in a 6-3 victory. Craig Gentry's third-inning single was the lone hit off Lester, who is 3-1 with a 2.20 ERA in his last five matchups with the A's.
The left-hander has also been tough lately against all foes, going 4-1 over his last five starts with a 2.87 ERA. He limited Minnesota to one run and four hits over 6 1-3 innings in a 2-1 win Tuesday despite a 33-pitch first inning.
However, Lester has allowed 15 runs in 24 1-3 innings over his last four starts away from home.
Crisp, Josh Donaldson and Yoenis Cespedes are a combined 5 for 30 with 10 strikeouts against him. No current Oakland player with at least four at-bats has hit better than .250 against him.
The Red Sox (34-41) are batting just .195 with 1.9 runs per game during a 3-5 stretch, going 4 for 48 with runners in scoring position.
"We've had situations get away from us in terms of men in scoring position," manager John Farrell said. "We've got to continue to build opportunities. Whether or not we cash in on those, that's what we got to continue to focus on."
They haven't been swept in a four-game series since April 16-19, 2010, against Tampa Bay.
Boston faces left-hander Tommy Milone (5-3, 3.56), who has won a career-best five straight decisions over eight starts since suffering the loss in Lester's gem last month. He gave up six runs - all on three homers - in just four innings. He also surrendered three homers and was charged with seven earned runs in 4 2-3 innings of an 11-6 loss at Fenway Park since April 30, 2012.
David Ortiz has three home runs in four at-bats against him.
Milone yielded three runs over 5 2-3 innings in a 10-6 win over Texas on Tuesday.
"Every game I just try to stay within myself and not do too much," said Milone, who improved to 3-0 with a 2.30 ERA in his last seven home starts dating back to last season. "I'm trying to get those guys out and so far it's been working."
Derek Norris' status is uncertain after he sat out Saturday's contest with a bruised left forearm suffered on a foul tip in Friday's win. He's 1 for 9 in his last three games but had hit .458 in his previous seven with nine RBIs.