A day after lefty Scott Kazmir allowed four runs on nine hits in 4 2/3 innings, right-hander Jesse Chavez surrendered four runs on 10 hits in five innings.
Meanwhile, A's batters struck out 10 times and stranded seven on base, going 0-for-5 with runners in scoring position on Saturday.
"The starting pitching has really been what's carrying us to where we can get decent at-bats, score runs and win," said A's manager Bob Melvin. "There are times the offense has to pick up the starters, too."
Chavez's streak of 16 consecutive innings without an earned run allowed, achieved over his previous two starts, came to a halt quickly Saturday. The right-hander served up a 2-1 line-drive base hit to Brock Holt with one out in the first, and Hanley Ramirez promptly launched a long home run to center for a 2-0 Red Sox lead.
Chavez was on the hook for two more runs in the third, when Ramirez caused trouble again with a two-out infield single and scored on David Ortiz's ensuing double in advance of a Mike Napoli RBI single.
Chavez had to work around two baserunners in each of the next two innings before his departure at 98 pitches.
"They put good at-bats together," said Chavez. "They didn't chase when I had two strikes. They made me come back over the plate, and it resulted in me pitching out of jams. That's what a good lineup and a good team will do to you."
"The only small difference I saw was he was a little bit up," said catcher Stephen Vogt. "Typically, if he makes a mistake over the plate, it's down, and today he made a couple out and over the plate that he doesn't do, so that was a little different. But if you go back and watch, he still made some good pitches.
"We've still won nine out of 14. That's how we gotta look at it. Nine out of 14 is pretty good, considering where we were."
Jane Lee is a reporter for MLB.com. Follow her on Twitter @JaneMLB and listen to her podcast. This story was not subject to the approval of Major League Baseball or its clubs.