To answer the original question, it has happened only once, in 2006.
In 224 chances before this season, only three #4-seeds have won a regional.
2006 - Missouri beat #1 (and host) Pepperdine in regional final (Missouri had to beat Pepperdine twice)
2008 - Fresno St. beat #2 San Diego in regional final (SD had to beat Fresno twice)
2012 - Stony Brook beat #2 Central FL in regional final (Stony Brook had to beat UCF twice)