Duchscherer (6-4) won for the third time in four starts and improved to 5-0 at the Coliseum, getting a five-run lead after the third inning. Cust hit a two-run single during a six-run burst in the third.
"It was nice to get a big lead for Duch and have him work the way he does -- fast -- and get back in the dugout," Cust said.
The Athletics trailed 1-0 when an error by first baseman Jason Giambi allowed Travis Buck to reach leading off the third. A bunt single by Jack Hannahan with one out set up Bobby Crosby's tying double. Cust put the A's ahead, Mark Ellis hit an RBI single and Carlos Gonzalez capped it with a two-run double.
"That six-run inning was something we hadn't done for a while," manager Bob Geren said. "We hadn't linked hits together. It was nice to see."
Cust singled home another run in the fourth and Eric Chavez's second hit of the game chased Rasner after only 3 2/3 innings, his shortest outing of the year.
Every Oakland player reached base and every starter but Buck had a hit. Rasner (3-4) lost his fourth straight start.
Giambi hit his 15th homer of the season and drove in another run against his former team during a three-run ninth. New York fell back to the .500 mark (33-33).
"We seem to take a couple steps forward and then take a couple steps back," Yankees manager Joe Girardi said. "That's frustrating because we're a better team than what we've showed. Some days it's our offense, some days it's our pitching. It's a combined effort. "
Duchscherer allowed one run and five hits in seven strong innings, struck out four and walked one. He has allowed only five earned runs over his last four starts.
Duchscherer struck out Alex Rodriguez on a nasty 72 mph curveball to end the first -- the first of A-Rod's three K's in an 0-for-4 night.
"He changes speeds. He locates his cutter very well, his fastball very well, his curveball very well," Girardi said. "He lives on the corners and he doesn't make a lot of mistakes. He's got unbelievable control and he can throw any pitch at any time, and it makes him tough."
Giambi's towering shot over the scoreboard in right field was the first home run surrendered by Duchscherer in seven starts. He had gone 41 2/3 innings without giving up a longball.
Duchscherer actually ran into Giambi on the steps to the batting cage Tuesday and the pitcher asked the slugger to keep any of his hits inside the fences. Giambi now has three home runs off Duchscherer.
"I told him yesterday, 'No more home runs off me,' then he hit a home run," Duchscherer said. "I don't think he listened."
Giambi connected in the second for his 192nd home run while with New York, tying him with Tino Martinez for 14th place on the Yankees' list. It was Giambi's 379th homer overall and that moved him to 56th all-time along with Orlando Cepeda and Tony Perez.
The Yankees had scored only one run in each of the last three games Rasner started. This time, he didn't give New York much of a chance -- he was tagged for career highs of seven runs and nine hits.
What went wrong?
"Everything," he said. "Giving up six hits in a row is kind of tough. I threw some good pitches, I threw some bad pitches. They seemed to hit everything and pretty much found every hole out there. I had to pay for everything."
New York RHP Phil Hughes, on the DL with a stress fracture of a right rib, was scheduled to undergo X-rays and could begin a throwing program soon. ... Yankees RHP Andrew Brackman, already on the 60-day DL while recovering from Tommy John surgery, underwent an appendectomy Tuesday. ... A's RHP Joey Devine, on the DL since May 30 with inflammation in his right elbow, expects to being playing light catch Friday. He woke up pain-free Tuesday and again Wednesday and will go off his anti-inflammatory medication soon.