The European Tour said Barnes, who had cancer, died on Monday with family members by his side.
Barnes played in six Ryder Cups between 1969 and 1979. He is most known for beating Nicklaus in the final day morning singles, and then again in the afternoon at the 1975 Ryder Cup at at Laurel Valley, Pennsylvania.
After being beaten by Barnes, Nicklaus demanded a rematch, telling US captain Arnold Palmer to put him up against Barnes again.
On the first tee of the afternoon singles, Nicklaus, who was then the reigning Masters champion, told Barnes "You've beaten me once, but there ain't no way you're going to beat me again". Barnes went on to beat Nicklaus 2 and 1 having earlier won 4 and 2 in the morning singles.
"The Americans couldn't believe it," said Bernard Gallacher, Barnes' good friend and Ryder Cup partner, "and they were all congratulating him saying they never thought anybody could beat Jack."
Away from the Ryder Cup, Barnes -- known for playing with a pipe in his mouth and a bottle of vodka and orange juice in his bag -- won nine titles on the European Tour and achieved a fifth place finish at the 1972 Open.
Barnes finished inside the top 10 of the European Tour's Order of Merit every season from 1972 -- the first year of the tour -- to 1978.
"He will always be rightly remembered for defeating Jack twice in one day in 1975," said David Williams, chairman of the European Tour, "but his impact was felt far beyond that as one of the tour's great characters and entertainers, something which endured throughout his career on the Senior Tour."
Barnes won the Senior British Open at Royal Portrush in 1995 and 1996.
Barnes liked a drink and famously marked his ball on the final hole of the 1982 Scottish Professional Championship with a beer can, before putting out for the win. He received treatment for alcoholism in 1993.
The Associated Press contributed to this report.