The 28-year-old Scot won all three of his rubbers over the weekend to finish the 2015 campaign with 11 wins against no losses.
That was second only to John McEnroe's prefect 12-0 in 1982, a year after the elite World Group was introduced.
Murray won the first set with ease, but was taken all the way in the second before charging back from an early break in the third to clinch the win for Britain.