The custom-built Vox instrument, used by the late rockers at the height of the Fab Four's fame, was snapped up by an unidentified buyer at the Music Icons sale at the Hard Rock Cafe in Manhattan.
Bosses at Julien's Auctions previously predicted the guitar would fetch between $200,000 and $300,000 (£129,000-£194,000).
The instrument, which sold just a few years ago by Christie's Auction House for little more than $100,000 (£65,000), was played by Harrison while rehearsing I Am The Walrus, and by Lennon during a video session for the song Hello, Goodbye.
Both tracks were included on the Beatles' 1967 album Magical Mystery Tour.
Other highlights of Saturday's auction included a stage jumpsuit worn by David Cassidy, which sold for $18,750 (£12,097) and Conway Twitty's 1957 Gretsch Guitar, which went for $23,750 (£15,323).
A slew of Elvis Presley memorabilia also proved to be big draws - his Hagstrom Electric Guitar went under the hammer for $50,000 (£32,258), while a pair of shoes inscribed and worn by the King sold for $46,875 (£30,242), and the pants the legend sported in the video for Jailhouse Rock collected $12,500 (£8,065).