I always thought it was the Roger Staubach pass.
From the Pro Football Hall of Fame web site interview with Staubach:
“...’It was 14-10 at the time and time was running out. When I threw the ball to Pearson, I kind of under-threw it. The term “Hail Mary” was developed because after the game, I told the press I closed my eyes and said a “Hail Mary.”’
https://www.profootballhof.com/news/chat-transcript-with-roger-staubach
I knew it had to come from someone before Flutie... Thanks for teaching me!