UAB didn't record a field goal in the first 4:55, but trailed just 7-4 at that point when Hakeem Baxter scored the first bucket of the night for the Blazers. Marshall only made two baskets in the final seven minutes of the half and trailed at intermission 31-22.
Cokley made a layup, then a three-point play to give the Blazers a 14-point lead with 14:16 to go. The lead reached 20 with 5:17 left on a pair of free throws by Lee, who was 7 of 9 from the line.
Justin Edmonds led Marshall (9-18, 5-9) with 11 points.