Galloway's 3-pointer pushed the Explorers' lead to 25-12.
Boise State went scoreless for more than three minutes in the first half, and La Salle took advantage.
Consecutive baskets by Garland gave the Explorers a 12-point lead. Garland's perfectly placed lob pass resulted in a thunderous dunk by Galloway to make the score 31-17.
Drmic scored 11 points in the first half as Boise State tried to stay close. The Broncos trailed by eight points at halftime.
La Salle shot 63.3 percent from the field and 52.4 percent from 3-point range, something Boise State was unable to overcome.
"We worked hard to get here," Galloway said. "We want to make a run. We want to show that La Salle can play with the best teams in the country. We're here to make a statement."
NOTES: Boise State earned the school's first at-large NCAA Tournament bid. Its previous berths resulted from winning the Big Sky and Western Athletic Conference tournaments. ... Wednesday was the 59th anniversary of the Explorers' 92-76 win over Bradley in the 1954 NCAA championship game. .. The First Four matchup was the first meeting between Boise State and La Salle.