Mathews's men won the second Test by 100 runs after paceman Shaminda Eranga dismissed England No 11 James Anderson with the penultimate ball of Tuesday's final day.
Victory saw Sri Lanka take the two-match contest 1-0, after they had clung on for a draw in the first Test at Lord's with just one wicket standing, and represented their first major series win outside of Asia since they triumphed in New Zealand in 1995.
It was the first time Sri Lanka had won a Test campaign in England comprising more than one match and was the perfect riposte to Vaughan, who had damned the Lankan bowlers as "a glorified county attack".
Mathews, named man-of-the-match in Leeds after Test-best contributions with both bat (160) and ball (four for 44 in England's first innings), savoured a dramatic success.
"It was an amazing victory. After the first Test went down to the wire, to the last ball, today (Tuesday) went to the last over as well," said Mathews, who also made a hundred at Lord's.
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