Davis finished with 12 points while Steve McElvene scored 10 with nine rebounds and four blocked shots for Dayton (9-2), which has won four of its last five.
Cooke hit back-to-back 3-pointers to put the Flyers up 62-56 with 3:19 to play. Miami scored seven straight to take a one-point lead with 1:35 left and neither team scored until Cooke found Davis for the winner.
Eric Washington, who led Miami (6-6) with 15 points and five assists, missed a potential winning 3 as time expired.
Dayton took its biggest lead, 52-41, on a jumper by John Crosby with 10:35 remaining but the Redhawks used a 15-4 run to make it 56-all before Cooke's 3s.