Andre Hollins added 13 points for the Golden Gophers (20-14), who play the winner between Miami and Valparaiso in the second round.
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.
Earl Pettis scored 19 points for La Salle (21-13), while Ramon Galloway added 13 and Jerrell Wright 12. It was the first postseason game for the Explorers since they qualified for the NCAA tournament in 1992.
This was the 14th appearance for Minnesota in the NIT, including championships in 1993 and '98 - but the '98 title has since been vacated.