The 13th-seeded Explorers (22-9) play fourth-seeded Kansas State on Friday in Kansas City.
Ramon Galloway, one of the Atlantic 10's top scorers, added 21 points in a fast-paced offense that did pretty much whatever it wanted. The Explorers shot a season-high 63 percent from the field - 16 of 22 in the second half.
Garland went 9 of 11 from the field - his best shooting game of the season - and the Explorers were 11 of 21 behind the arc.
"It's an unbelievable feeling," Garland said. "When I came here, coach (John Giannini) told me I could help him win games and get him to the next step."
Thirteenth-seeded Boise State (21-11) got its first at-large bid and was looking for the first NCAA tournament win in its history. The Broncos were up to it in a game of top-this shooting, falling to 0-6 in the tournament.
Anthony Drmic had a game-high 28 points for the Broncos, who shot 49 percent but trailed most of the way.
La Salle is back in the tournament for the first time since 1992, a 21-year span that included a rape scandal involving three players. The men's and women's basketball coaches were fired over it in 2004, and Giannini came in to dig out the program.
Giannini led the Explorers to back-to-back 20-win seasons for the first time since 1988-90. His first coaching appearance in the NCAA tournament completed the rebuilding and came 59 years after La Salle beat Bradley 92-76 for the 1954 NCAA title - in Kansas City, no less.
His guards led the way.
"I recruited Ty really, really hard out of high school, and I told him, 'This is why I chased you all over the place, to win NCAA tournament games and see if you could be a great player,'" Giannini said. "I knew he could do it."
Although the two teams had never played, they felt like they knew each other from somewhere. They saw mirror images of themselves as they watched videos in preparation for the game - two teams that use four guards, taking an uncommonly small approach to a big man's game.
La Salle's best is the 6-foot-3 Galloway, who was second in the Atlantic 10 with 17 points per game. He's taken on a bigger role since 6-foot-11 center Steve Zack sprained his left foot in early March, sidelining him indefinitely. Zack was on crutches Wednesday, towering over the rest of the Explorers during warmups.
Boise State follows the lead of Drmic (17.3 points) and Derrick Marks (16.3), who formed the highest-scoring guard tandem in the Mountain West. The Broncos will sometimes put five guards on the floor, opting for speed over size.
The Broncos' concession to size got them going early. Six-foot-9 forward Ryan Watkins scored their first three baskets, getting the ball inside. La Salle went with its slick guards, who quickly settled in behind the arc.
Sam Mills hit three 3s, Galloway scored his first points off a drive to the basket, and Garland and D.J. Peterson made layups for a 22-12 midway through the first half, prompting Boise State to call a timeout.
The Explorers would never be seriously threatened again.
Coming out of the timeout, Galloway took a charge from Watkins under the basket, then went down the court and hit a 3. Garland's alley-oop pass to Galloway for a dunk off a fast break gave La Salle its biggest lead, 31-17, with 5:24 left in the half. La Salle led 35-27 at the break.
Six-foot-8 forward Jerrell Wright - the Explorers' inside threat - scored four baskets in the first five minutes of the second half, keeping La Salle in control. Mills' 3-pointer extended the lead back to 14 points with 14 minutes to go.
Drmic kept the Broncos in the game, scoring 14 points in the first 10 minutes of the second half. But Boise State couldn't stop La Salle's balanced offense long enough to make a run until the closing minutes.
Marks' pull-up jumper cut it to 74-68 with 1:51 left, the closest the Broncos had been since the opening minute of the second half. The comeback ended there.