Pablo Sandoval and Alejandro De Aza hit solo shots off Archer in the second and David Ortiz followed suit with a two-run blast in the fourth. Sandoval added a sacrifice fly in the sixth that put the Red Sox up, 5-1.
"They seemed like decent pitches, not great," said Archer of the home runs. "Still probably considered mistakes.
"... I didn't pitch bad. I just made a couple of mistakes and they capitalized. That's what big league hitters do."
Archer allowed five earned runs on five hits and a walk in six innings. And, as a reminder that Archer still was Archer, he notched 10 strikeouts, giving him double-digit whiffs for the fifth time this season.
"I thought Arch was really good," Rays manager Kevin Cash said. "Six innings, 10 punchouts, five hits. The home run just kind of beat us up a litle bit.
"If you look at the stat line, it's basically the same thing. They connected on three home runs, which is unusual given what he's done. But everything else was the same. Fastball velocity, command, really good. Slider was really good."
Archer is 1-6 with a 5.48 ERA in nine career starts against the Red Sox, compared to 28-18 with a 2.88 ERA in 69 career appearances (67 starts) against all other opponents.
Archer took his first loss since May 7 against the Rangers, snapping a career-high six-game winning streak.
"You can't be perfect every time you go out," Archer said. "Make the most of the game situation. Keep it as close as possible. ... I think I did a good job of doing that. It stinks because my goal is a team win every time.
"I felt like I had good stuff. But good hitters capitalize on pitches that are not well executed. That happens. Turn the page. I'm focused on my next outing."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.