Langevine, who was 9 of 10 from the field and 7 of 10 from the foul line, also grabbed 12 rebounds for the Rams (17-14), who will play top-seeded VCU in the quarterfinals Friday.
The Rams scored the first six points, four by Langevine, and never trailed. It was close through the first 10 minutes but with Langevine scoring eight points, Rhode Island went on a 16-3 run to build a 32-22 lead at the half.
Fatts Russell added 19 points, and Jeff Downtin chipped in with 12.
Saul Phiri led the Explorers (10-21) with 10 points. No other player scored in double figures for LaSalle.
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