La Salle's victory ended the opening four games of the event that were played over two days and served as a prelude to the avalanche of action that begins Thursday.
The Explorers moved into the second round against fourth-seeded Kansas State, a game that will be played Friday in Kansas City, Mo..
La Salle shot 63 percent from the floor and went 11-of-21 from 3-point range. Garland was 9-of-11 and hit two of La Salle's 11 3-pointers.
Ramon Galloway added 21 points for the Explorers (22-9), who were seeded fourth going into the Atlantic 10 Tournament and lost in the quarterfinals to Butler. This was La Salle's first NCAA victory since 1990.
Anthony Drmic put on a one-man show for Boise State, hitting five 3-pointers and scoring 28 points. The Broncos finished at 21-11, having fallen in the quarterfinals of the Mountain West Conference Tournament to San Diego State.
The NCAA Tournament's second round of 32 games will be conducted over the next two days beginning at 12:15 p.m. EDT with Michigan State taking on Valparaiso in Auburn Hills, Mich.