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.
"The big key is not walking anybody," Chavez said. "Today, even if I did go to a full count I didn't want to give in."
Beltran homered off reliever Ryan Cook in the seventh.
Brett Gardner also homered for New York, a two-run shot in the ninth. The Yankees put two more runners on base after that against struggling reliever Jim Johnson, and Luke Gregerson came on for the last out.
Jeter played his last scheduled game at the Coliseum and received a lengthy ovation from the sold-out crowd that included several thousand fans decked out in Yankees jerseys. The retiring shortstop was given a bottle of Northern California wine during a pregame ceremony and received a financial donation from the A's for his Turn 2 Foundation.
It was at the Coliseum, in fact, where Jeter made one of the most memorable plays of his career. His backhanded flip to the plate helped save the Yankees in the 2001 playoffs.
Jeter hit a sacrifice fly with the bases loaded in the seventh before being replaced by Brendan Ryan in the bottom half of the inning.
Nuno, who had allowed only three earned runs total over his previous two outings, allowed eight runs and eight hits in three-plus innings.
<b>NOTES: </b>Norris also hit a three-run home run on Mother's Day. .<th>.<th>. The 10 runs were the A's most against the Yankees since 2007 and helped them snap out of a weeklong power slump. Oakland had hit only one home run over its previous five games. .<th>.<th>. A's OF <b>Josh Reddick </b>(hyperextended knee) will begin a rehab assignment with Triple-A Sacramento on Tuesday. .<th>.<th>. Oakland LHP <b>Drew Pomeranz </b>(5-3) pitches against visiting Texas on Monday night.