Cokley knocked down 10 of 13 shots from the field while the Blazers hit 35 of 57 from the floor (61.4 percent).
Zack Bryant scored 18 points and dished off eight assists and William Lee finished with 12 points, five boards and two blocked shots while Jalen Perry added 11 points off the UAB bench.
J.D. Notae led Jacksonville with 18 points and Devin Harris added 16 points and five assists.
Tanner Rubio got the Dolphins within five points midway through the first half with a jumper that made it 21-16, but UAB responded with a 14-2 run over the next six minutes to make it 35-18 with five minutes left in the first half.
UAB hosts Chattanooga Monday.
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