Graduate student Nijel Pack led the Hurricanes (3-1) in scoring with 17 points, while senior Brandon Johnson paced Miami on the boards, hauling in seven rebounds.
Drake got off to a hot start, taking an early 17-8 lead thanks in part to a 10-point first half from guard Bennett Stirtz.
The Hurricanes strung together a 10-2 run late in the frame to cut the deficit to five points with three minutes to play in the half, but Drake recorded back-to-back layups in the final minute of the first half to take a 36-27 lead into halftime.
Johnson went to work for the Hurricanes in the second half, scoring all seven of his points in the final 20 minutes. An old-fashioned three-point play for the forward at the 12:52 mark pulled the Hurricanes to within four, 44-40, of the Bulldogs.
However, Miami faced foul trouble early in the second half, sending the Bulldogs to the line three times in a three-minute span, which allowed Drake to extend its lead back to double-figures, 53-42, with nine minutes to play.
The Hurricanes shot 50 percent from the field in the second half, but ultimately could not complete the comeback, falling 80-69 to Drake.
Miami will face the loser of the Oklahoma State/FAU game on Friday at 2 p.m. ET at TD Arena.
