Winning the playoff match on outdoor red clay means the U.S. will remain in the World Group, the top tier of the Davis Cup. Colombia was trying to qualify for the first time.
"A lot of work and a lot of sacrifice went into this," Fish said. "A year ago today I wouldn't have been able to do this. I fought as hard as I could."
Fish also became the first American to win three times in a single Davis Cup match since Pete Sampras in the 1995 final in Moscow. Fish won in Friday's opening singles and teamed up with John Isner to win the doubles on Saturday.
It was a sweet exit for retiring American captain Patrick McEnroe, whose team battled with the 8,700 feet in altitude, a determined Colombia team and the absence of top players like Andy Roddick, James Blake and the imposing doubles team of Bob Bryan and Mike Bryan.
"What a Herculean effort from Mardy this weekend," McEnroe said. "Mardy's was one of the greatest efforts in Davis cup history -- forget my 10 years as captain. To win three points in these conditions -- with the altitude, the crowd and everything. He is in illustrious company.
"I couldn't have asked for a better way to end my captaincy," McEnroe said.
Giraldo broke Fish in the final set to lead 6-5, needing only to serve out to force a deciding fifth match. Fish broke back to level at 6-6, though, held his serve by fighting off two break points and then broke the Colombian again for the 8-6 victory in 4 hours, 5 minutes.
Fish logged 11 hours of tennis in winning two singles matches and a doubles match.
"It was as tough a relegation match as we could have had with the altitude, the balls and a quality opponent," Fish said. "To win three points in one Davis Cup match under these circumstance ... is one of the biggest -- if not the biggest -- accomplishment of my career."
Ryan Harrison was scheduled to play the final match for the United States, but it wouldn't have affected the outcome and was canceled due to a late rainstorm. In an interesting twist, Andy Roddick made his debut in the Davis Cup in 2001 in McEnroe's first match as captain. The debut for Harrison would have come as McEnroe exits.
The U.S. has dropped out only once since the World Group began in 1981. The Americans have won the Davis Cup a record 32 times, the last in 2007 -- McEnroe's only title as captain.
Fish said the match against Colombia proved the U.S. has enough depth to compete.
"We have a lot of guys who can play well on a lot of surfaces -- myself, John, Sam [Querrey], Andy, James and the Bryans," Fish said. "We wish we had six or eight spots to take everyone."