Radcliffe, 19, is best known for playing wizard Harry Potter in the blockbuster film franchise.
In Peter Shaffer's "Equus," he portrays a troubled young man who blinds six horses. Richard Griffiths plays the psychiatrist who treats him.
The BBC said Close, Turner and Cooper were in the audience when the play opened Thursday night at New York's Broadhurst Theatre.
"He's not a kid anymore," Griffiths told the British broadcaster. "He's a young man and he deserves whatever breaks that brings."
In the show, Radcliffe appears nude at one point, something that caused considerable buzz when the film star headlined the London production of the play last year.
"If it's in the play, if it's in the story, if it's necessary, then it's right," Turner told the BBC about doing nude scenes on stage. "The fact that he's willing to learn and risk is all to his credit."
The New York Times's drama critic Ben Brantley praised both Radcliffe and Griffiths in his review, noting they performed with "sensitivity and intelligence."
"Mr. Griffiths and Mr. Radcliffe are delivering utterly credible and often affecting performances," Brantley said.