NEW YORK - Jose Contreras dreamed of these moments.

First he pitched six shutout innings against one of his team's biggest rivals, then he got to hug and kiss his family after they watched him pitch in the major leagues for the first time.

Making his first start since his wife and children defected from Cuba last week, Contreras struck out a career-high 10, leading the New York Yankees to an 8-1 victory over the Mets on Sunday in the opener of a day-night doubleheader sweep.

"I thought my dad was going to win," 11-year-old Naylan Contreras said.

At a tender news conference between the first game and the Yankees' 11-6 victory at night, Contreras was accompanied by wife Miriam and their two daughters. While Naylan sat on her mother's lap, the pitcher sat next to them holding 3-year-old Naylenis, repeatedly kissing her head and squeezing her after she nodded off and fell asleep.

He dedicated his win to his family and to "the people of Cuba who support me."

"During the game, I didn't think about my family," he said through a translator. "I concentrated on getting one out after another. I knew after the game my family would be here."

And that presence, he said, "gave me more motivation."

Contreras stifled the Mets on two hits until cramps in his forearm and thumb forced him out three pitches into the seventh. He frustrated the Mets so much that Ty Wigginton broke his bat in half after he struck out in the third inning.

Signed to a $32 million, four-year contract after defecting from Cuba in October 2002, Contreras (5-3) has been maddeningly inconsistent. He often talked of how much he missed his family, and Yankees manager Joe Torre said that his family situation might have contributed to his trouble adjusting.

Contreras' family left Cuba on a 31-foot boat a week earlier and were captured by U.S. Border Patrol agents on Big Pine Key, Fla., last Monday. Contreras was reunited with them a day later in Miami Beach, and they looked on from a luxury suite on a sunny summer afternoon. His youngest daughter ate cotton candy.

"It tasted great," she said, also through a translator.

He allowed a single to Jose Reyes, his first batter, who promptly was caught stealing by catcher John Flaherty. Contreras then retired 10 in a row - including four straight on strikeouts. Mike Cameron got the Mets' second hit, a leadoff single in the fifth, but he, too, was thrown out at second.

Contreras then walked the bases loaded - the four walks tied his career high - but he got out of trouble when Kaz Matsui flied out on a 3-2 pitch.

"I was very tense," Miriam Contreras said. "As the game progressed and Jose was striking batters out, I was able to relax a little bit."

Contreras said the cramp was not serious and came from throwing forkballs. Derek Jeter, who had the fourth multihomer game of his career, wasn't concerned at all about Contreras' results.

"To be honest with you, I don't care how he pitched," Jeter said. "I'm just happy for him. He's got a big smile on his face."