It was Drakeās first victory against an ACC opponent since topping Wake Forest 77-74 in its second game of the 2017-18 season.
Stirtz was the only player for either team in double-figure scoring with 11 minutes remaining in the second half.
Nijel Pack became the first Florida State player to reach double digits when he made a 3-pointer with 6:54 remaining to pull within 56-47, but Stirtz answered at the other end with a three-point play to restore a 12-point lead.
Stirtz hustled in transition to throw down a putback dunk to give Drake a 65-54 lead. Mitch Mascari added a wide open 3-pointer with 22 left and he made a steal at the other end to seal it.
Mascari finished with 15 points for Drake (4-.
Pack scored 17 points for Miami (3-1). Jalen Blackmon and Matthew Cleveland each added 12.
The Bulldogs entered ranked fourth in Division I in scoring defense, allowing opponents just 51.0 points per game. Miami entered averaging 98 ppg.