Moreland hit a go-ahead, two-run single in the seventh inning and drove in three runs, helping the Red Sox rally to a 7-5 victory over the Tampa Bay Rays on Sunday.
"The group of guys in here just make it easy," Moreland said. "It's been a smooth transition. When you have that, you get pretty comfortable, pretty quick."
Moreland, signed as a free agent to a $5.5 million, one-year deal, has gone 16 for 33 after opening hitless in 12 at-bats.
"He's put together a number of quality at-bats of late," Boston manager John Farrell said.
Red Sox slugger Hanley Ramirez advanced from first to second on Moreland's hit and limped off with what Boston called a left hamstring cramp.
"I'll be fine," Ramirez said. "I'll be in there tomorrow."
Pablo Sandoval had a two-run homer for the Red Sox, who won their second straight after losing five of eight. Mookie Betts and Christian Vazquez each had three hits.
Vazquez added an RBI double in the eighth against Austin Pruitt.
Joe Kelly (2-0) allowed one hit in 2 2/3 scoreless innings, and Craig Kimbrel struck out two in a perfect ninth for his fifth save.
Brad Miller had a two-run triple, and Tim Beckham and Corey Dickerson hit solo homers for the Rays, who have lost five of six heading into Monday morning's Patriots' Day finale of the four-game series.
Tampa Bay had taken a 3-0 lead in the first.
"It was a little bit of a frustrating loss," manager Kevin Cash said. "We had a few opportunities, but were unable to hold the lead."
Beckham homered in the fifth for a 5-4 lead against starter Drew Pomeranz, who allowed five runs and five hits in 4 1/3 innings with 10 strikeouts.
Sandoval had tied the score 4-4 in the third when he homered off Alex Cobb, who gave up four runs and 11 hits in five innings. Panda jumped a couple of times to celebrate with teammates on his way back to the dugout.
"It was a weird one," Cobb said. "Some situations that I put myself into or things didn't go your way happened."
Rays: RHP Jake Odorizzi went on the 10-day DL, a day after he strained his left hamstring. RHP Chase Whitley was recalled from Triple-A Durham.
Red Sox: CF Jackie Bradley Jr., on the 10-day DL with a sprained right knee, is scheduled to start in pair of games at Triple-A Pawtucket during an injury rehabilitation assignment before he is activated. ... Dustin Pedroia fouled a ball off his left ankle, limped around but stayed in the game.
Pomeranz threw his first seven pitches of the game for balls and got a mock cheer when he threw a strike. He also had a wild pitch.
Cobb failed to strike out any batters for the first time in 89 career major league starts.
"I think it comes back to not getting any strikeouts," he said of his outing. "You've got to have times in the game where you can rely on that swing and miss pitch. I just didn't have it today."
Betts hasn't struck out in 119 plate appearances, the majors' longest stretch since Juan Pierre -- then with Florida -- went 147 in a row in 2004.
Rays: LHP Blake Snell (0-1, 3.18 ERA) is slated to start the series finale.
Red Sox: Knuckleballer Steven Wright (0-1, 13.50) is set to start Monday in his first outing since giving up four homers in 1 1/3 innings against Baltimore.