The group — including John Lennon’s widow Yoko Ono and the estate of George Harrison — claims the record company improperly 'pocketed millions of dollars' in music royalties.
They have now been given the right to take EMI and its affiliate Capitol Records to court in an attempt to win back the money.
They are also claiming over £13 million in damages and are attempting to reclaim the rights to all of their master recordings.
"It’s a great win for us," said Beatles lawyer Paul LiCalsi after New York State Supreme Court Justice Karla Moskowitz denied EMI’s request that the case be thrown out.
The dispute with EMI dates back to 1979, when the Beatles — including their company Apple — alleged that the companies had underpaid the band by more than £10.5 million.
A settlement was reached in that case in 1989, Mr LiCalsi said, granting the band and Apple increased royalty rates.
But he said a recent audit had uncovered fraud.
According to the group, EMI and Capitol wrongly classified copies of Beatles recordings as destroyed or damaged, and secretly sold them.
When the band launched the lawsuit Apple Corp chief Neil Aspinall said: "We have tried to reach a settlement and regret our efforts have been in vain."
In 1991, Apple won a High Court ruling preventing EMI from releasing a box set of two Beatles albums.