Andre Hollins added 13 points for the Golden Gophers (20-14), who play Miami in the second round after the Hurricanes beat Valparaiso 66-50.
"I am impressed," Smith said of his young team. "All year long, we've been in every game. Overall, we've been right there. Now, we're starting to make some of these steps."
The Gophers closed with a 15-6 run to give coach Tubby Smith his 100th win at the school. Only seven coaches in the program's history have won at least 100 games.
"I really didn't realize it," Smith said of the milestone. "You're so involved in the game."
It was the first postseason game for the Explorers since they qualified for the NCAA tournament in 1992. La Salle's 21 wins are the most for the program since a 30-2 finish in 1990.
"I love my kids," coach John Giannini said. "They did a lot of good things this year. We just had some bad performances and it was the wrong time to do it."
This was the 14th appearance for Minnesota in the NIT, including championships in 1993 and `98 -- but the `98 title has since been vacated.