The only cite I will use is my own memory. I distictly remember Staubach calling it a Hail Mary pass in the after game interview and then explaining that he meant that he threw it and then began praying that it would be caught. The comment greatly ammused my father and made an impression on me even though it came from a hated Cowboy.
As promised, an update.
Barry Popik, the premier searcher of databases, found a 1972 cite, which he posted to the American Dialect Society Mailing List after my 1974 find.
It also was a quote involving Staubach, from the Sporting News. It was a quote from his Navy coach, Wayne Hardin.
Hail Mary was also used by late Laker announcer Chick Hearn to refer to a last second desperation shot in basketball.