The rookie Puig, trying to bust his way into an outfield filled with All-Stars, also singled twice and tripled, and stole a base. He's batting .489 with a team-high 10 RBIs. His monster two-run homer in the first inning was immediately followed by Jerry Hairston's solo shot off Oakland starter Dan Straily.
Capuano held the A's scoreless until Cespedes lined his homer over the wall in left-center leading off the fifth inning.
Puig, the $42 million signing last summer, didn't hustle out of the batter's box on his fifth-inning single and was thrown out at second trying to stretch by Cespedes, who initially misplayed the shallow fly, but Puig made up for it by legging out a triple to lead off the bottom of the seventh. Had Puig recorded the double in the fifth, he would have hit for the cycle.
The Dodgers added to their lead in the fifth inning off reliever Jordan Norberto, with Nick Punto's infield single plating a run that was unearned because of shortstop Hiroyuki Nakajima's fielding error.
Capuano, on the bubble to stay in the rotation with a pre-game ERA of 10.61, was removed after 5 2/3 innings having allowed five hits and one walk, with four strikeouts.
Mark Lowe inherited two runners from Capuano and retired Cespedes on a popout to end the sixth inning.
Up next: The A's will enjoy an off-day on Wednesday, but righty Bartolo Colon will pitch in a Minor League game to remain on schedule. Come Thursday, it's lefty Brett Anderson taking the mound in Goodyear for a road contest with the Reds, who will start right-hander Johnny Cueto. Closer Grant Balfour, who has been recovering from minor surgery on his knee, is scheduled to make his Cactus League debut in the game.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.