After a dismal first half, St. Joseph's built a 15-point lead early in the second and barely withheld a late Dayton surge to seal a 60-57 win, its first at UD Arena since 2001.
After Dayton came back to tie the score at 57 with 11 seconds left, St. Joseph's had time for one last play. That set up Galloway's clutch shot.
"Everybody knew they wanted me to have the ball, so they ran the play for me," Galloway said. "I came off of that second screen, I saw my man backing up, and I knew I had an inch. That's all I needed to get a shot off."
In the first 20 minutes, the Hawks (14-6, 4-2 Atlantic Ten) looked as if they had left their offense at home. They shot just 7 of 26 from the field and 3 of 13 from long distance.
The usually prolific scoring trio of Galloway, Ronald Roberts Jr., and Halil Kanacevic, who averaged 17.5, 14.1, and 11 points per game entering the game, combined for just seven points before halftime.
Chris Wilson finished with 15 points and Galloway and Roberts had 12 for the Hawks.
"I think Dayton played very good defense and I thought we settled a lot," St. Joe's coach Phil Martelli said. "We played a lot of sideline-to-sideline and not a lot of rim-to-rim, and we missed a lot of layups."
Trailing by 25-20, St. Joseph's seemed to find its scoring touch after halftime. The Hawks shot 73.7 percent in the second half, but Dayton still pulled within four with less than a minute left.
"We worked hard for 40 minutes and we worked hard for two days prior to those 40 minutes getting ready for Dayton, and we'll take it," Martelli said. "Certainly, we've had them go the other way against us. Road wins are a really big deal."