Palmer reached double figures for the 41st straight game, tying the school record, and Watt finished with 14 points and 13 rebounds for and the Islanders (11-8), who ran their winning streak to six.
Matt Mierzycki led the Broncs (3-18) with 14 points.
Corpus Christi opened the second half on a 14-5 run to build their largest lead, 46-23. A 3-pointer by ChaRunn Jones cut Pan American's deficit to 58-46 with less than four minutes to play, but the Broncs never got any closer.
The Islanders ended the first half on a 19-4 run for a 32-18 halftime lead.