The win is the Trojans second-straight over a Conference USA opponent after knocking off Western Kentucky, 87-81 on Sunday.
Zack Bryant hit a 3-pointer to put the Blazers up, 72-69 with 1:13 left, but Varnado answered with a 3. Bryant hit the first of two from the line to make it 73-72 with :31 remaining, but UAB missed three straight free throws. Varnado drilled a jumper for the lead with :11 left and Hicks blocked a Bryant layup at the buzzer.
Varnado finished with a career-high 32 points and Hicks contributed 10 points, 10 rebounds and three blocked shots for Troy (6-5).
Bryant led UAB (7-5) with 18 points. Lewis Sullivan added 15 points.
Military academy athletes can get waivers to delay service, go pro
Athletes from U.S. military academies who want to immediately go pro can now do so pending approval from the defense secretary. They also must eventually fulfill their military obligation or repay the cost of their college education.
No. 9 Virginia desperate to find deep stroke vs. Columbia
No. 9 Virginia outscored its first two opponents by a combined 45 points despite shooting 16 percent from 3-point distance.
What James Wiseman's ineligibility means for Memphis
James Wiseman was ruled ineligible Thursday. His return to Memphis is uncertain. How talented are the Tigers without him?