OAKLAND, Calif. » Sleep-deprived first-time father Kurt Suzuki didn’t realize how tired he truly was until hitting a wall in the fifth inning.

He had already done plenty in his first game since welcoming his newborn daughter, Malia.

“It was good to be back out here. It had been a long couple days,” Suzuki said. “I was running on Adrenalin.”

Suzuki came off the paternity leave list and delivered a go-ahead RBI single to help Trevor Cahill stay unbeaten and the Oakland Athletics topped the Texas Rangers 3-1 last night.

Cahill (4-0) overcame a three-walk first inning to pitch seven scoreless innings against the rival Rangers, who kicked off a seven-game West Coast road trip all against the division with a punchless performance to lose for the fourth time in five games. Texas fell into a first-place tie with the Los Angeles Angels in the AL West.

Grant Balfour pitched the eighth and Brian Fuentes finished for his seventh save in nine chances after allowing Michael Young’s two-out RBI single.

“We had runners out there and we just needed a base hit at the right time,” said Rangers manager Ron Washington, who lost on his 59th birthday. “It would have been the difference in the ballgame. We didn’t get it. Even against Trevor we had bases loaded, runners on second and third and just didn’t get a hit off him at the right time.”

Cahill outdueled C.J. Wilson (3-1) and quickly found his rhythm after escaping his 26-pitch first inning unscathed. Cahill, who on April 11 received a new five-year contract worth $30.5 million, issued three free passes in an inning for the fifth time in his career but the first since July 17, 2009, against the Angels during his rookie season.

“Walking three guys in the first inning put things in perspective: ’I’ve got to throw strikes,’ ” Cahill said. “I just started pounding the zone a little bit more.”

Cahill had walked only eight batters total in his first five starts this season before the four total walks yesterday. The right-hander allowed seven hits and also struck out four while improving to 7-2 for his career against Texas.

Mitch Moreland, Young and Elvis Andrus each had two hits for Texas, which has gained or lost ground in the division race each of the last 14 days after holding a two-game lead for three straight days from April 13 to 15.

Suzuki did some early catching work in the bullpen to get back in a groove, but he started at designated hitter. Manager Bob Geren said Suzuki would be back behind the plate today. His two-out RBI single in the third put the A’s ahead, then Josh Willingham added an RBI double in the fifth. Suzuki also grounded into a fielder’s choice in the seventh as Oakland’s third run against Wilson came home.

Suzuki left Anaheim on Wednesday to return to the Bay Area, where his wife, Renee, gave birth to the couple’s first child Thursday morning. Malia weighed in at 8 pounds, 3 ounces.

“It’s an exciting time in anybody’s life,” Geren said. “He was all smiles today. He was looking forward to coming back to work.”

Regular A’s DH Hideki Matsui had the night off against a lefty starter but was slated to start today.

Oakland played its first game back home since the venue was named the Overstock.com Coliseum this week.

“I still call it the Coliseum,” quipped Washington, a longtime A’s third base coach before taking the Texas job.

Texas clinched the club’s first AL West title since 1999 at the Coliseum last Sept. 25 and went on to reach the franchise’s first World Series before losing to the San Francisco Giants in five games.