Rock fans were treated to a diva-licious Fiona Apple performance yesterday, as the 22-year-old rocker stormed off a New York stage after blurting out obscenities at her ticked-off audience. The waifish singer appeared before 3,200 people — including Gwyneth Paltrow and Apple’s boyfriend, “Magnolia” writer-director Paul Thomas Anderson — who had paid $27.50 each to see her performance. But 45 minutes into her concert, Apple collapsed onstage, buried her face in her hands and began to sob. (A similar meltdown reportedly took place at last year’s MTV Awards.) The band attempted to pick up the slack by breaking into “Carrion” (from Apple’s debut album, “Tidal”), but Apple soon exploded again. “All you critics out there better not (expletive) tear me apart or I’ll (expletive) kill you,” she warned. She then ordered the band to stop. “This song is dead! Just stop it! This is a nightmare!” she cried before announcing she’d take a five-minute break and then return. But she never came back. The audience was told to go home, but that the singer would do a make-up concert.