With fees, the buyer paid £6,100, and a collection of four autographs from the band, each inscribed to "Kathy" - the fan to whom the key belonged - sold for a total of £5,124.
Chris Albury, director at Dominic Winter Auctioneers, said the level of competition during the bidding "demonstrates that the Beatles' popularity remains as strong as ever".
"What makes these particular pieces so extraordinary is the deeply personal links to the band and to the people and places that formed part of their story," he said.
"The 20 Forthlin Road key is an example; it has a remarkable provenance stretching back to 1965 and provides a tangible connection to Paul McCartney's family home and to one of the most important addresses in Beatles history.
"To see it sell for £6,100 for three times its low estimate after such strong bidding was a fantastic result."
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