La Salle coach John Giannini would not offer specifics about Galloway's mother other than to say she has been going through "real serious issues."
"I really admire how he stepped up today in the face of personal adversity," Giannini said. "Not everyone wants to have everyone know everything going on in their lives, but he's a very positive person. Like a lot of us, he's going through a tough stretch. I admire him more than ever for the way he's responded."
Galloway, a 6-foot-3 senior, did not start the game but played 34 minutes off the bench. He scored six points, 11 below his average, but the final two were the most important in recent La Salle history.
It gave Big Five teams back-to-back upsets of top-10 teams on consecutive nights, with Villanova having defeated No. 5 Louisville on Tuesday.
The Explorers ended Butler's 13-game winning streak. The Bulldogs played without leading scorer Rotnei Clarke, who missed the game with a neck injury.
La Salle (13-5, 3-2 Atlantic Ten) was led by Tyreek Duren with 16 points, 6 assists, and 3 steals.
Andrew Smith, who scored the last 11 points for Butler (16-3, 3-1), sank a layup with 8.4 seconds to play for a 53-52 lead. With no timeouts remaining for either side, the ball was inbounded to Galloway, who looked to the bench and saw Giannini give him the "Go" sign.
"I hesitated a little bit, and I guess when I made that little hesitation when I stopped and looked at Coach G, the defender kind of relaxed a little bit," Galloway said. "Then I kind of got past him and made the layup."
Roosevelt Jones' heave from just short of half-court went off the backboard and rim, and the celebration began - but prematurely. Butler coach Brad Stevens asked the officials to check whether the clock had started properly when La Salle inbounded after Smith's final basket, and the court was cleared.
But a review showed the clock functions were correct, and it was celebration time, part two.
"We have to feel tremendous about getting a hard-earned victory against a special opponent like that," Giannini said. "But that being said, I'm not overly surprised . . . in fact, I'm not surprised at all. I think our players are good."
Contact Joe Juliano at firstname.lastname@example.org, or follow on Twitter @joejulesinq.