Skelton, the last British winner of the King's Cup with his victory in 1999, had held the advantage with the fastest four-fault total on Russel in the two rounds of the contest until Welles, the last to jump, completed a deliberate clear on 10-year-old Armani.
This was Welles' first visit to Hickstead as a competitor. He considered it "a huge honour to win such a historic class".
David McPherson jumped the only other clear round on the impressive Bob's Diamond. He carried four faults forward from his first effort, but nevertheless finished in third place - ahead of two other Britons - Robert Whitaker on Nicolette II and 19-year-old Tim Gredley on Fabriana.
Welles' win left Britain with the sad record of having won just a single International class through Scott Smith and Cabri d'Elle during the four-day meeting.
Laura Kraut had earlier become the fourth United States rider to receive the Queen Elizabeth II Cup after riding her long-standing partner, the 14-year-old Anthem, to the only clear round of the four-horse jump-off.Reuse content