Robinson Cano also homered for the Yankees, who won their fourth straight game. Pitching in front of about 200 family members and friends, local product CC Sabathia tossed seven sharp innings to log his first victory in three starts.
But the star of the afternoon was Teixeira, who hit a solo fourth-inning homer and laced a two-run single in the fifth off former teammate Bartolo Colon, who allowed six runs in six innings.
Teixeira added a shift-beating hit in the eighth before homering off Graham Godfrey in the ninth, a two-run shot, giving him his eighth of the season.
"It's what we've always known he's capable of doing," Yankees manager Joe Girardi said. "Tex is another guy who can carry your club for a while; that's how hot he can get. He swung the bat great today."
Home run hitting is vital for the Yankees, who are 25-11 when hitting at least one home run. They are 0-10 in games without a homer.
"When you can hit a home run, it's instant offense," Teixeira said. "It makes your team feel good, it pumps everybody up, whether it's a solo shot or a grand slam. Chicks dig the long ball. Fans dig the long ball. Yeah, I said it. It's fun hitting home runs because not everyone can do it."
New York utilized an aggressive approach against Colon, having seen the hurler throw heat around the strike zone during his surprising comeback season with the Yankees last year.
"We all know he throws a lot of fastballs, so you want to be able to not miss a pitch when he throws it over the plate," said Cano, who slugged a long solo homer to start the offense in the second inning.
Derek Jeter laced a run-scoring single in the third inning for his 3,153rd career hit, breaking a tie with Paul Waner for 15th on the all-time list. Jeter later legged out a bunt single to tie George Brett for 14th place with 3,154 hits.
Alex Rodriguez also had a sacrifice fly for the Yankees, who have won eight consecutive games in Oakland, their longest streak since the facility opened in 1968.
"With a team like this, you throw the ball in the middle of the plate, they make you pay," Athletics manager Bob Melvin said. "With the depth in their lineup power-wise, it's going to go out of the park."
The pride of nearby Vallejo, Calif., Sabathia has always had mixed results pitching at the Coliseum, where he paid to watch his hometown A's as a child and still holds season tickets for the Raiders.
That held true in the early going on Saturday, as Jonny Gomes stroked a run-scoring single in the first inning and Sabathia pitched out of a bases-loaded jam in the second by inducing a fielder's choice.
"[My] command got a little off and [the] fastball command wasn't there, so I was just trying to make some pitches and stay behind the ball," Sabathia said. "I was able to get it back later in the game."
Josh Reddick unloaded on a long solo home run facing Sabathia in the third to tie the score, but the left-hander settled in after that, keeping Oakland off the board the rest of the way.
"His ball was cutting a little today early on," Girardi said. "I didn't think he had command of it down and away early on. He found it and that's when he sailed through."
Sabathia walked two and struck out four in his first start at the Coliseum since July 6, 2010, when he also beat the A's. He improved to 4-5 in 12 career starts there.
"It always feels good to be able to come home and pitch in front of the family," Sabathia said.
Arguably nobody left the Coliseum feeling better than Teixeira, though, who has cleared his mind and is showing promise that he could be getting back on track for another of his 30-homer, 100-RBIs campaigns after all.
Having mostly shaken the cough from his inflamed airways -- though he had to pause during a postgame interview to chug from a water bottle -- Teixeira has hit three homers and is 6-for-10 since the Yankees arrived in California.
"I'm glad I'm seeing some results, because then you'd probably be asking me what's my next plan," Teixeira said. "I'm just being real aggressive with my swings, trying to let it go, which I've done my whole career."