NEW YORK — The New York Yankees could have had Paul Byrd earlier this month when he cleared waivers. Last night, they may have had second thoughts about passing on the opportunity.

Byrd, obtained by the Red Sox in a deal with the Cleveland Indians on Aug. 12, pitched six strong innings against the Yankees and helped the Red Sox to a rather easy 11-3 defeat of New York.

“I hadn’t really thought about it exactly like that,” confessed Byrd after limiting the Yanks to two runs on five hits to register his second win in three starts since joining the Sox. “I heard that the Yankees were interested and just didn’t pull the trigger. But I wasn’t thinking about that on the mound, trying to show them that they should have picked me up or anything like that.

“I’m just glad somebody wanted to take a chance on me. I haven’t had the best year and I was more interested in proving the Red Sox right. When somebody puts their faith in me, brings me over in a not-too-great year and wants me to help their team in a playoff run, it feels really good to go out there and give a good performance and help the team win.”

Byrd was nicked for a run in the first on an RBI double by Alex Rodriguez in the first, then yielded a run-scoring single to Robinson Cano in the fourth. Other than that, he was fairly efficient.

“Early in the game,” manager Terry Francona said, “I thought he threw aggressively in to left-handed hitters, then threw his breaking ball effectively to the other side. That opened up both sides of the plate for him. He did his job.”

Byrd’s stuff doesn’t overmatch hitters. But he uses experience, intelligence and precise command to keep opposing batters off balance.

“And what’s been great to see,” added pitching coach John Farrell, “is how quickly he and Jason [Varitek, catcher] have been able to establish a relationship out there. That allows him to do what he does — in and out, up and down — and just follow the plan.

“He has no fear of contact and no fear of the strike zone.”

After last night, he can also claim a distinction. He became the first pitcher since Steve Trachsel in 2000 to beat the Yankees for two different teams in the same season. As a member of the Indians, he defeated the Yankees on April 25.

smcadam@projo.com