Teixeira remained home in the New York area after his wife gave birth to the couple's third child, William Charles Teixeira, earlier Tuesday.
"Tex and Leigh had a baby boy today and we're all happy for him," manager Joe Girardi said.
Lance Berkman, acquired from Houston last month, started at first base and played for the first time in his home state wearing a uniform other than the Astros. It was only his second start at first base for the Yankees after six starts as the designated hitter.
New York also opened the short series matching division leaders without second baseman Robinson Cano, whose .329 batting average was fifth in the American League, in the starting lineup.
When he arrived at the ballpark, Cano told Girardi that he was sick and was taken out of the original lineup. Ramiro Pena started in his place, but Cano pinch-hit for him in the sixth inning and stayed in the game.
Before the game, Cano said he took some medicine and would see how he felt later.
Girardi said Teixeira, who now has two sons and a daughter, would rejoin the Yankees sometime during their series at Kansas City that begins Thursday. That means Teixeira will have to wait until mid-September to play in Texas, where he began his career with the Rangers from 2003-07. Teixeira, who had played in all of his team's 111 games before Tuesday, leads the team in home runs with 26 and is second to Alex Rodriguez in RBIs with 85. He has been especially hot in August, with 5 HRs and 11 RBIs in eight games.
With Cano out, Ramiro Pena took his spot at second base. Cano was supposed to bat fifth, but Girardi moved everybody who was behind him up a spot in the order and put Pena ninth.
"I took some medicine and I'll see how I feel later," Cano said.
Berkman was born in Waco, Texas, went to college at Rice University in Houston and was the first-round pick by the Astros in 1997. He made his major league debut in 1999 and was a five-time All-Star with full no-trade rights. He approved the deal to go to the Yankees.
"If I was going to have to leave Houston, I wanted it to be a unique opportunity," the 34-year-old Berkman said. "It was like getting called up. It's great to get a chance to play for the Yankees. ... It felt a lot like when I walked into the clubhouse in the Astrodome in '99, when I didn't know anybody and wanted to feel like I was part of the team."
Berkman said his father was a big Yankee fan but that he wouldn't characterize himself that way while growing up in central Texas.
"I was a Don Mattingly fan," Berkman said. "I didn't have a team I followed, but Don Mattingly was a player I followed."
When Astros general manager Ed Wade called Berkman about the possibility of a trade, there were eight teams on the list. Berkman said no to San Francisco, the Los Angeles Angels, Detroit and the Chicago White Sox. Beside the Yankees, he said he would have considered Boston, San Diego and the Rangers.
"It was an unreal experience. I never thought it would be a reality. I didn't think they'd trade Roy [Oswalt]. So this was like a death in the family," he said. "I could have said I didn't want to be traded. But the reality was maybe I was in a little bit of a rut mentally in Houston because we were having such a poor season. ... I felt it would be good to come to a place where there was a high standard of excellence."
Information from ESPNNewYork.com's Wallace Matthews and The Associated Press was used in this report.