Gio Gonzalez (9-6) worked six innings for the win, allowing seven hits and four runs with three strikeouts and a pair of walks. Michael Wuertz turned in a scoreless ninth for his second save.
Adrian Beltre went 3-for-4 with a two-run homer and drove in three for the Red Sox, who stumbled to their fifth loss in seven contests.
Activated from the 15-day disabled list prior to the game after recovering from a strained left hamstring, Clay Buchholz (10-5) was shelled in defeat for six hits and five runs, fanning two with three walks over four-plus frames.
Jed Lowrie's one-out run-scoring hit in the fifth got the Sox within a run, but the A's chased Buchholz in the home half, scoring three times to take a 6-2 advantage.
Kurt Suzuki and Cust stroked back-to-back hits before Scott Atchison took the hill. He allowed a one-out RBI single from Mark Ellis, then after a passed ball moved both runners into scoring position, Davis stroked a two-run hit to center before being caught in a rundown between first and second.
Beltre's two-run homer to right-center in the sixth made it 6-4, but Boston couldn't score with two on in the seventh. Neither could the A's extend their advantage, as Davis flied out with the bases loaded in the home half.
Oakland's Coco Crisp hit a one-out triple in the eighth but was erased at home trying to score on a fly to left from Cliff Pennington.
The failed attempt at an insurance run wasn't costly, though, as Wuertz set down the side in order in the ninth to lock up the victory.
Boston picked up a run in the first after a Beltre RBI single, then Watson knotted the score in the second with a one-out solo shot.
In the home third, Daric Barton reached on a leadoff infield single and scored on Cust's two-run blast two batters later.
Watson had played in 36 previous MLB games with the Mets (2003) and A's (2005; 2010) and went 75 career at-bats before going deep...The Sox head to Seattle for four games starting Thursday, continuing their 10-day, 10-game western road swing...Oakland improved to 22-10 this season in day games...The A's host the White Sox for three starting Friday...Boston also activated Lowrie off the 60-day disabled list, designated infielder Ryan Shealy for assignment, while optioning pitchers Dustin Richardson and Fernando Cabrera to Triple-A Pawtucket.