Rice, a redshirt junior, also had a career high 10 rebounds to lead Illinois (6-0), which has not lost in its last 25 November games. UNLV had a chance to win, but Kevin Olekaibe's desperation 3-pointer from the right corner rattled off the rim for the Rebels (2-3), who were held scoreless in the final 4:16.
Khem Birch led the Rebels with 12 points, 10 rebounds and 4 blocks. Bryce Dejean-Jones added 11 points, while Olekaibe had 10. Nnanna Egwu added 12 points for Illinois.
UNLV's Roscoe Smith, the nation's leading rebounder averaging 16.3 per game, had 13 boards.
Trailing 39-29 at halftime, the Illini scored second half's first five points and eventually took a 51-49 lead.