Making his Angels debut on four hours' sleep with some jet lag thrown into the equation, Teixeira was hitless in four at-bats with a walk. He was acquired from the Braves on Tuesday in exchange for Casey Kotchman and Stephen Marek.
Beckett's high-octane stuff made the Angels' production against him -- 11 hits, eight runs (seven earned) in 5 1/3 innings -- all the more impressive to Teixeira, who accounted for two of the October hero's eight strikeouts.
"I thought he had really good stuff," Teiexeira said. "I had my troubles with him. You've got to give our hitters credit."
Teixeira lashed a 400-foot out to dead center in the first inning. He reached on first baseman Kevin Youkilis' error in the sixth and was walked in the eighth.
"I knew after that first line drive my first at-bat that it might be a tough night," he said, grinning. "But there's no reason for me to press, and I wasn't pressing tonight. It just wasn't my night.
"I know once I get settled in, we're going to start rolling."
Teixeira was true to his Gold Glove reputation, making all the plays behind Joe Saunders, Justin Speier and Darren Oliver.
"I feel good, comfortable," said Torii Hunter, who bashed his 17th homer while Garret Anderson was triggering the attack with a homer (No. 11) among four hits and four RBIs. "Now that's what we're trying to do with Mark Teixeira.
"We just want Mark to feel comfortable, let him know he doesn't have to do it all here. Once he does, believe me, he's going to do some damage. I've seen it. Running after balls he's hit, chasing them down, I've lost a lot of weight."
Teixeira is looking forward to getting back into a more normal routine in New York, with four games starting Thursday night at Yankee Stadium.
"It was a short night, that's for sure," Teixeira said. "I spent most of my time packing, getting ready to make my flight early this morning. It'll be nice to get into New York and start a normal baseball life again."
He admitted there "definitely were some nerves," grinning when it was suggested it was like the first day in a new school.
"You play in one place the whole year, in Atlanta," he said. "I was comfortable there. But to come here and get a win, get those nerves out of the way, is huge for me. To finish up a sweep against the Red Sox is a nice feeling."
Teixeira will find that he's playing for one of the game's most patient managers in Mike Scioscia, a man not known overreact to a performance -- good, bad or indifferent.
"There's so much we're trying to get him acclimated with in our system," Scioscia said. "He's getting in the flow. I didn't see any jitters.
"Beckett's got great stuff, and he threw some really tough breaking balls to Mark and struck him out a couple of times. Mark fits right in; I think he feels good. It's good to get the first game out of the way and let him get some at-bats under his belt. He's going to be important in our lineup.
"Mark is a guy who certainly can work counts. Right now, we're trying to feed Vlad [Guerrero] and Torii and Garret, and putting Mark ahead of those guys [in the No. 3 spot] makes sense. His on-base percentage from both sides of the plate can really help us."
Scioscia can't wait to see his new switch-hitter bust out. The Yankees will have Andy Pettitte on the mound on Thursday night, turning Teixeira around to the right side, where he's a .305 career hitter compared to .275 from the left side.
Against Pettitte, he's batting .474 with 19 at-bats.
"This guy's one of the top talents in baseball," Scioscia said. "We know Mark [primarily] from the other dugout. Talking to players who have been around him, he's an incredible competitor."