The Bulldogs had won 13 games in a row since Nov. 21, but let a five-point halftime lead slip away and fell for the first time in Atlantic 10 Conference play.
La Salle took a 52-51 lead with 32 seconds to play on jumper by Sam Mills, but Butler moved back in front with 8 seconds left on Andrew Smith's layup.
Galloway then took the inbounds pass and drove the length of the floor to produce the winning points.
Tyreek Duren led the Explorers with 16 points, five rebounds and six assists. La Salle hit just 41 percent of its shots, made only four free throws and was outrebounded as well. The Explorers, however, forced 13 turnovers and committed just eight.
La Salle improved to 13-5 for the season and to 3-2 in conference play. The Explorers had not defeated a team from the Top 10 in 33 seasons.
Butler (16-3, 3-1) got 16 points from Smith and 15 from Kellen Dunham.