Lee Mazzilli, Lou Piniella and Dave Winfield homered, and four pitchers held Kansas City to 10 hits last night as New York swept a doubleheader from the Royals, 2-0 and 4-3, in Yankee Stadium.

Rudy May, making his first start since May 26, had a three-hit shutout for seven innings of the second game before Don Slaught led off the eighth with his third home run of the season. Two outs later, U.L. Washington beat out a topped roller and May (5-3) was replaced by Lynn McGlothen. He gave up a two-run homer to Hal McRae, his 21st of the season, which made him the first player in the majors to drive in 100 runs this season.

"It's been a long time since I was out there that long," said May. "I'm a little tired, but one thing about it: I got a win, I went 7 2/3 innings and I'll be okay in the morning."

Rich Gossage, who saved the opener for Dave Righetti, also pitched the final inning of the second game to earn his 25th save this year.

In the opener, Mazzilli, a former Met, celebrated his return to New York with a two-run homer in the sixth inning. Righetti and Gossage limited the Royals on four singles.

Afterward, Gossage said he was disgusted by the negative atmosphere in New York. "Negativism is like injected into you," said Gossage, who was referred to in one paper as "The Wild Goose" after his loss Sunday in Comiskey Park. "It's just very upsetting . . . You battle the people upstairs in the office, you battle everybody from your paper boy down to the front office."