Rafael Devers hit his eighth home run in the fourth and Mookie Betts hit his 15th, a two-run shot in the fifth. Andrew Benintendi followed Betts' with his fourth, and the Red Sox took a 4-1 lead.
"Just keeping it in the park -- that's been a challenge for us in the starting-pitching department," manager Buck Showalter said. "I thought he pitched Betts well and just made one mistake on him. It's just the execution of the pitches. They're hitting mistakes that we're throwing, and it's been a challenge for us keeping it in the park."
Bundy's catcher, Chance Sisco, was pleased with how he threw.
"He had really good stuff tonight," Sisco said. "For the most part, he was commanding his stuff, locating his pitches good with two strikes. Those three pitches that were in the zone, they kind of put the barrel on."
The Orioles scored in the third against Rick Porcello (6-1) when Jonathan Schoop's sacrifice fly scored Sisco and closed the gap to 4-3 in the sixth on Pedro Alvarez's two-run homer, his eighth.
Bundy (2-6), who yielded to Tanner Scott in the seventh, allowed four runs on five hits in six innings. Scott gave up a two-run single to Benintendi that put the Red Sox ahead 6-3.
The Orioles struck out 13 times against Porcello, Joe Kelly, Matt Barnes and Craig Kimbrel.
"It's something we've been challenged with and when you face even better pitching," Showalter said. "You look at the guys they ran out there at the end [and] the starting pitching. That's why you make commitments like that to those type of people. They're good pitchers."
MOMENT THAT MATTERED After the Orioles closed to within 4-3, Scott walked his first two hitters, Sandy Leon and Jackie Bradley Jr. in the seventh. After Betts flied out, both runners moved up a base and scored on Benintendi's single.
"If we could have got a shutdown inning there," Showalter lamented. "Tanner just couldn't find the plate."
HE SAID IT "There was a seven-, eight-inning outing there, but the next thing you know he's thrown almost 30 pitches in the first inning. But he settled in there good. Dylan, it's tough for me to fault much with him. I thought he had good stuff, threw it over in a tough venue and a really tough night to pitch condition-wise." -- Showalter on Bundy's struggles in the scoreless first and his outing on a night when the game-time temperature was 50 degrees with intermittent rain
UP NEXT David Hess will be recalled from Triple-A Norfolk to start against the Red Sox on Sunday at Fenway Park. Hess, who won his Major League debut in the first game of a doubleheader against the Rays on May 12, takes on Eduardo Rodriguez at 1:05 p.m. ET.
Rich Dubroff is a contributor to MLB.com based in Boston.