Murray, whose heroics helped clinch the title against Belgium last year, was pegged back after taking the first two sets, but eventually prevailed against the world number six 7-5 7-6(6) 3-6 4-6 6-3 in four hours and 54 minutes.
It was Murray's first event back on court since the birth of his daughter, but any doubts over his fitness were dispelled as he once again carried Britain's hopes almost single-handedly, winning three matches, including the doubles, in three days.
"I am lost for words at this stage; he (Murray) is a man of steel, isn't he?" Britain's captain Leon Smith said.
"What Andy managed to do was astonishing since he hasn't played since the Australian Open final."
After his exertions, Murray said he was keen to get back to his family.
"It's (wife) Kim's first Mother's Day, so it will be nice to get to see her this evening. I'll try to get back for bath time and to put her to sleep -- the baby, not Kim."
Murray has been dogged by the shadow of Fred Perry for much of his career, but victory over Nishikori allowed him to put another Perry milestone behind him.
Having become the first British man since Perry to win a grand slam and then Wimbledon, Murray surpassed the former great by improving his unbeaten streak in Davis Cup singles and doubles rubbers to 14.
The win was the joint-longest match of Murray's career along with his 2012 U.S. Open final triumph against Novak Djokovic, who he will now face in the quarter-finals in Serbia in July.
World number one Djokovic was also involved in an epic tussle on Sunday and took almost five hours to beat Mikhail Kukushkin in five sets.
That drew Serbia level at 2-2 against Kazakhstan before Viktor Troicki finished off the tie by beating Aleksandr Nedovyesov in the deciding rubber.
(Reporting by Toby Davis; editing by Ken Ferris; editing by xxx)
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