Rivers, 9-for-12 from the floor, scored eight consecutive points in the second half to give the Tigers their biggest lead of the game, 78-51.
Terrence Oglesby also had 21 points for Clemson (9-0), and Raymond Sykes and Trevor Booker added 11 points each.
Steven Ramirez led Puerto Rico-Mayaguez (1-11) with 21 points and seven assists.
In their first game after a two-week break for exams, the Tigers led by only two points, 25-23, with less than 7 minutes to play in the first half, but pulled away for a 46-37 halftime advantage.
The Tigers put the game out of reach in the second half with a 13-0 run that included two 3-pointers and a layup from Rivers that put them ahead 78-51 with 9:20 remaining.
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