Garcia-Mendoza scored consecutive field goals late in the second half and Mouzy's 3-pointer with 2:01 remaining gave the Trojans a 70-60 lead and secured their fourth straight win.
Chuck Guy and Solomon Bozeman finished with 12 points each for the Trojans (12-9, 4-2 Sun Belt Conference).
Florida International rallied from a 43-28 halftime deficit with a 15-4 run in the first 4:09 of the second half. Marvin Roberts and Phil Gary each had three-point plays and Allen's basket with 15:51 remaining capped the spurt and put the Panthers within 47-43.
Arkansas-Little Rock responded with six unanswered points in the next 3:50.
Allen led Florida International (8-10, 3-3) with a game-high 18 points.