Yoenis Cespedes drove in two runs and Josh Donaldson snapped an 0-for-33 slump with an RBI single.
Chavez (6-4) carried a shutout into the sixth.
With the second-best record in the majors behind San Francisco, the A's have won three of four and are off to their best start in nearly 25 years.
"It's good to see," Oakland manager Bob Melvin said of his club's power surge. "We haven't been swinging the bat as well as we were earlier, certainly on the power portion of it. But two big three-run homers today gets you off to a good start."
Norris, who matched his career high with three hits, homered in the first and Crisp connected in the second off Nuno (1-3).
Carlos Beltran hit his first home run for the Yankees since coming off the disabled list. But the All-Star veteran also was called out on a strange play in the eighth inning when he lost track of the outs and wandered away from first base.
With one out in the eighth and the A's ahead 10-3, Beltran grounded into a forceout at second. He trotted toward New York's first-base dugout and got halfway there, then turned around and headed back toward the bag — Beltran was tagged in foul ground.
Umpire Dan Iassogna made the call and Yankees manager Joe Girardi came onto the field for a brief discussion. By rule 7.08, Beltran was out for "abandoning" the base.
"I thought there were two outs," Beltran said in the Yankees' quiet clubhouse. "It was too late to go back."
Chavez blanked the Yankees until Derek Jeter doubled in the sixth and scored on Mark Teixeira's two-out single. Oakland's right-hander was stellar otherwise, allowing five hits over six innings with four strikeouts.