The teams met in the Coaches vs. Cancer Classic, played at the new Barclays Arena in Brooklyn. St. Joseph's will play Florida State for the tournament title on Saturday while Notre Dame will face Brigham Young in the third-place game.
St. Joseph's scored the final eight points of the second half, holding Notre Dame scoreless over the final 4 minutes.
Galloway's reverse layup with 1:43 to go forged a 66-66 tie.
The Hawks then held the Fighting Irish without a point for the first 3:49 of the extra period and Ronald Roberts scored seven of St. Joseph's 13 overtime points.
Roberts finished with 21 points and 14 rebounds and Chris Wilson added 19 points for St. Joseph's (2-0).
Jack Cooley led Notre Dame (2-1) with 14 points and 14 rebounds.