BOSTON -- A half hour before Wednesday's game, the Red Sox at last had a lineup.

The holdup? They had to wait for their newest first baseman Dominic Smith to pass his physical so they could activate him.

In a par-for-the-course night for the injury-riddled yet resilient Red Sox, Smith joined the club on short notice and chipped in with an RBI single in his new team's 6-2 victory over the Giants at Fenway Park.

Undermanned as they are, the Red Sox (18-13) continue to find ways to win. Manager Alex Cora's team has won four in a row and eight of its last 11, even with 14 players on the injured list.

"It just goes to show the culture that they build here, and the foundation that Alex has," said Smith. "Obviously, Raffy [Devers] has been here and his leadership and it just goes to show they have a next man up mentality."

Once again, starting pitching was a key factor. Kutter Crawford (2-1, 1.56 ERA) went a career-high seven innings. He allowed four hits and two runs while walking two and striking out six.

As for Smith, the Rays officially released him from his Minor League deal on Tuesday, making him a free agent. They told him on Sunday that he could start seeking a Major League deal before his opt-out.

By Wednesday, he was at Fenway Park and starting at first base for the Red Sox.

"A whirlwind," said Smith. "Yeah, I didn't think I would be here, but I'm here. Very grateful for the opportunity.

"I found out yesterday, in the afternoon [about the pending deal], and then about the possibility that I'd be playing today, but I had to pass some physicals," said Smith. "I got here as quickly as I could. I got here late last night at like 2 a.m. And then woke up early this morning.

"Got my physical done and had a couple more in the afternoon and everything passed and at that point, it was just, 'Go play. Go do what you can and just try to get settled in."'

Smith's debut came one day after another first baseman -- Garrett Cooper -- played his first game for Boston. But Cooper got drilled on the right wrist by a pitch in his third at-bat on Tuesdays, so the Red Sox stayed away from him on Wednesday.

The Sox went on the fast track to get Smith activated, and medical clearance was the final hurdle. From there, he introduced himself to teammates and prepared to play baseball.

"A lot of them I didn't get to meet until I was out there on the field," Smith said. "A bunch of them came up to me, introduced themselves. It was fun seeing the success this ballclub has had from afar. It's pretty fun to just come and be a part of that."

In his third at-bat, Smith lined an RBI single to center for his first Red Sox hit. In the seventh, Giants third baseman Matt Chapman made a great play, taking a second hit away from Smith. There's no better way to feel part of a new team than to get a knock.

"It felt amazing," Smith said. "I've got plenty more where that came from but it was good to get that first one and have a first day like this, and now I can get settled in and help this ballclub win."

Given that Triston Casas [torn cartilage in his left ribcage] is on the 60-day injured list and can't play until June 21 at the earliest, the left-handed-hitting Smith and right-handed-hitting Cooper should both get their share of at-bats in the coming weeks.

"He's going to put together a good at-bat, just like Coop," said Cora. "We expect these two guys to help us. They slow down the game. They're gonna hit the ball the other way. It's great to add him to the roster."

Meanwhile, the barrage of injuries has had a bonding effect on the Red Sox.

"Obviously the first month hasn't been the greatest as far as keeping guys healthy," said Crawford. "Some freak things have happened, some stuff you can't control, but I think it just goes to show, no matter who we put out on the field, we believe in ourselves. We're showing resilience and belief in ourselves that we can go out there and compete no matter who we have on the field."