Oakland closed a 10-game road trip 5-5 and avoided its second three-game sweep in its last four series. The Athletics were swept at home by Texas April 21-23.
A.J. Pierzynski hit a solo homer for the Red Sox, who failed to reach .500 for the first time since the fourth game of the season.
Jed Lowrie had a two-out double off Chris Capuano (1-1) and after the bases were loaded with an intentional and regular walk, Cespedes beat out a slow roller to third against reliever Burke Badenhop.
Oakland closer Jim Johnson (3-2) got a double-play grounder by Jonny Gomes to end the ninth and worked the 10th for the win.
With the Red Sox trailing 2-1 in the seventh, Pierzynski homered into Boston's bullpen. It could have been worse for the Athletics when right fielder Reddick had trouble with pinch hitter Gomes' fly ball in the wind. He was charged with an error, allowing runners to reach second and third with one out. But reliever Fernando Abad got Jackie Bradley Jr.'s out at first on his attempted safety squeeze and Luke Gregerson retired Dustin Pedroia.
Boston starter John Lackey gave up two runs on five hits in six innings, walking three and striking out four.
Oakland's Sonny Gray also pitched six, giving up two runs and six hits, walking two with three strikeouts.
Cespedes gave Oakland a 2-1 edge in the sixth with an RBI double off the Green Monster. The Athletics grabbed a 1-0 lead in the first on Brandon Moss' two-out RBI single.
Grady Sizemore's RBI double tied it in the fifth, but Gray escaped a bases-loaded, one-out jam when Bradley bounced into a 1-2-3 double play.
In the third, Boston shortstop Xander Bogaerts' relay from shallow left cut down Donaldson trying to score. Crew chief Jeff Kellogg requested a replay review to see if catcher Pierzynski was illegally blocking the plate. Replays showed he moved his foot and blocked the corner just before he caught the throw, knocking Donaldson's foot away as it attempted to reach home. The play was upheld.
Oakland manager Bob Melvin challenged a call on the first pitch of the game — when Coco Crisp was called out on a 5-6-3 grounder. Replays were ruled inconclusive.
NOTES: Reddick limped off after grounding into a DP in the ninth and was replaced in the bottom of the inning. ... Boston DH David Ortiz played in his 1,999th career game. ... The Athletics open a 10-game homestand Monday when left-hander Scott Kazmir (4-0, 2.11 ERA) faces Seattle right-hander Chris Young (1-0, 3.04). ... The Red Sox are off Monday before beginning a two-game series on Tuesday against Cincinnati when lefty Felix Doubront (1-3, 5.70) goes against the Reds' Homer Bailey (2-2, 5.50). ... Sizemore went 2 for 2 before being pinch hit for, raising his career average to .321 (59 of 184) against the A's, his best against any AL team. ... The Red Sox held a pregame birthday party on the field for Wally their mascot. Mr. Met (New York Mets), the Oriole Bird (Baltimore) and Blades (Boston Bruins) were three of a handful of mascots on hand.