The first use cited in the Oxford English Dictionary is from Whitaker’s Almanack, 1900 (referring to the 1899 tournament):

“In their last match at Cardiff against Wales, Ireland won by a try to nothing, securing the triple crown with three straight victories as in 1894.”

The Irish victory in 1894 was reported as a Triple Crown by The Irish Times at the time and is possibly the first time the phrase was seen in print.

The phrase Triple Crown is also used in a number of other sports.