Senior forward Darryl Proctor (District Heights, Md.) added 20 points, while freshman wing Chauncey Gilliam (Columbia, Md.) scored 18 as UMBC won for the first time after five setbacks at Hartford.
UMBC led, 34-30 at halftime, and after an exchange of three-point field goals to start the second half, the Retrievers took control with a 13-2 run to lead, 50-35 with 14:40 remaining. The Hawks would whittle the deficit to nine points on two occasions, but Greene's long three with 7:44 to play restored the lead to 14 points at 64-50 and the advantage remaining in double figures the rest of the way.
UMBC hit 23 of 45 shots from the floor (51.1%), seven of 10 from behind the arc and 27 of 37 (73.0%) from the charity stripe. UH was just 21 of 58 (36.2%) from the floor and six of 23 from behind the arc.