The sought-after first-edition of Carroll's 1886 book Alice's Adventures Under Ground was given by the writer in January 1887 to Alexandra Kitchin, affectionately known as Xie.
The book was expected to fetch up to £3,000 after being put up for sale by the Duke of Gloucester to help pay his father's death duties.
But the rare volume, which was later developed into Alice's Adventures In Wonderland, was snapped up by a mystery buyer for £4,800 at Christie's on Thursday.
Xie's dad, George Kitchin, was the last dean of Durham Cathedral to govern Durham University, where he worked from 1908 until his death in 1912.
Xie was Carroll's favourite photographic model and he took at least 50 pictures of her.
When a friend asked the famous author how to take a wonderful photograph, Carroll replied: "Take a lens and put Xie before it."
Carroll, whose real name was Charles Lutwidge Dodgson, had many connections with Sunderland, and Whitburn in particular.
He made a number of visits to his cousin Margaret Wilcox, wife of the Collector of Customs in Sunderland, and lived in Highcroft, Whitburn, although his house no longer exists.
During his time in Whitburn, Carroll visited Whitburn Hall, home of Lady Hedworth Williamson, second cousin to Alice Liddell, to whom Carroll's most famous books are dedicated.
Here he met Frederika Liddell, another of Alice's cousins, whom he described as "one of the nicest children I have ever seen".
But the work most associated Carroll with Whitburn is the poem The Walrus and the Carpenter, which was claimed to be inspired by a stuffed walrus which was on display for many years at Sunderland's museum – although the famous exhibit only went on display after the publication of the poem.
Only the head of the museum's walrus remains, but a magnificent bronze statue in Mowbray Park still maintains the link.
In April 1869, Carroll's sister, Mary, married the Rev Charles Collingwood. Their home, the rectory at Southwick, now Holy Trinity, on Church Bank, has been recognised with a blue plaque and there is evidence that it too once housed a stuffed walrus.
Today, a statue of Lewis Carroll can be seen in Whitburn Library. It was moved from its original home in Cornthwaite Park after it was damaged.
The book was one of about 800 antiques and family treasures which the Duke of Gloucester sold for more than £3million at the auction.