"It's tough having only three innings, handing over that many innings to the bullpen and coming out of the game," Moore said. "It doesn't feel good, but I think it's days like this that make the good days the great days."
Moore, making sixth start since returning from the surgery in April 2014, gave up nine hits, walked one and fanned two. He's failed to go past five innings since his return.
"It's not fun right now, but I still believe in myself," he said. "I feel like when I was out there competing that that wasn't being timid."
Logan Forsythe hit a solo homer and two-run single for the Rays, who have lost five of seven.
The Rays bullpen didn't help, giving up five runs in five innings.
Travis Shaw hit his first two major league homers and went 4-for-4 with five runs scored and four RBIs for Boston.
Joe Kelly (3-6), demoted to the minors in late June for nearly a month, gave up five runs on nine hits in five-plus innings for his first victory since June 6.
Jean Machi earned a save in his Red Sox debut, getting the final four outs.
After having their six-run lead sliced to one, the Red Sox scored two runs on one hit in the sixth against reliever Steve Geltz. Castillo had a two-run single that made it 9-6, with Shaw making a nice slide by tapping the plate with his hand despite the throwing beating him.
Leading 1-0 in the second, they scored four on Castillo's RBI double, Brock Holt's sacrifice fly and Bogaerts' two-run double.
Shaw, recalled earlier Saturday, homered over the Rays' bullpen, making it 6-0 in the third. His second — a two-run shot — went into the center-field bleachers in the eighth.
The Rays crept back with two runs in both the fourth and fifth.
But Bogaerts' RBI single made it 7-4.
Rays: Steven Souza Jr. was hit by a fastball by Kelly and left in the sixth with a bruised left hand. "I dont know anything other than that hes getting an X-ray," manager Kevin Cash said. ... OF Desmond Jennings (left knee bursitis) continues his rehab at Triple-A Durham. He went 0-for-3 with two walks on Friday. ... Drew Smyly (torn left labrum) made his second rehab start Friday, giving up five runs in 3 1-3 innings.
Red Sox: 3B Pablo Sandoval missed his second straight game with a bruised left forearm after getting hit with a pitch Thursday.
WHAT A THROW
CF Kiermaier nailed the speedy Jackie Bradley Jr. at the plate on Shaw's single in the fifth.
The Rays gave up 16 hits, the most they've allowed against any AL East team this season.
Rays: RHP Nathan Karns (6-5) is scheduled to pitch the series finale on Sunday. He's made 15 starts giving up two or fewer runs, which entered Saturday tied for the AL's most.
Red Sox: Wade Miley (8-9) is slated to start when they close a 10-game homestand. He's 0-2 in his last five starts.