The Athletics, who have won nine of 10, outscored the Indians 30-6 in the series.
Oakland saved its best for the final game, pounding out 12 hits and drawing nine walks. Cespedes’ two-run double was the key hit in Oakland’s four-run fifth. He also drove in two runs with another double in the eighth.
Moss was 3 for 3 with two walks and scored four runs. He had an RBI double in the fifth, a two-run double in the sixth and a triple in the second.
John Jaso’s RBI double in the fourth put Oakland ahead for good while Josh Donaldson, who drove in seven runs in the series, had an RBI single in the fifth and scored four runs.
Jesse Chavez (4-1) gave up solo homers to Michael Bourn in the first and Michael Brantley in the fifth, accounting for both runs the right-hander allowed in five innings.
Cleveland has dropped four straight and six of eight. The Indians scored first in all three games, but were no match for Oakland, which leads the AL West with a 28-16 record.
Justin Masterson (2-3) allowed seven runs, seven hits and five walks in 4 1-3 innings.
Indians manager Terry Francona moved Nick Swisher and Carlos Santana, who have battled season-long slumps, down in the batting order, but the changes didn’t help the struggling offense, which has scored three runs or fewer 24 times in 44 games.
Santana was hitless in four at-bats while Swisher was 0 for 5 and committed an error in the seventh. Swisher fielded a routine grounder to end the inning and was given a sarcastic cheer by the small crowd of 14,872.
Third baseman Lonnie Chisenhall also had an error, giving the Indians a major-league high 45.
Bourn led off the game with a home run to center that landed in Cleveland’s bullpen, but the lead didn’t last long.
Moss started the second with a triple. Chisenhall fielded Cespedes’ ground ball and his throw landed in the camera bay behind first base. Cespedes was given an RBI.
Masterson walked Donaldson and Moss to start the fourth. Jaso’s one-out double put Oakland ahead and Josh Reddick followed with a single for a 3-1 lead.
Oakland put the game away in the fifth, stringing together four hits and a walk off Masterson. Following Donaldson’s RBI single, Moss drove in a run with a double and Cespedes’ double scored two more.
Jaso and Reddick also drove in two runs apiece.
Oakland shortstop Jed Lowrie left the game in the second inning because of a strained neck and was replaced by Nick Punto.
NOTES: Bourn’s homer was the eighth of his career leading off a game and the first for the Indians this season. ... Cespedes, who has had a hamstring injury, was the DH on Sunday. ... Oakland manager Bob Melvin said LHP Scott Kazmir, ejected in the second inning Saturday, will likely stay on his regular turn and start Friday in Toronto. ... Indians SS Asdrubal Cabrera had the day off. ... Oakland LHP Joe Savery will go on the paternity list Monday. The Athletics open a three-game series at the Rays on Tuesday.