Down 15-14 in the first half, Toledo (6-0) went on a 24-8 run and never trailed the remainder of the game. Florida Atlantic (1-6) twice cut the deficit to 8 in the second half but Toledo pulled away.
The Rockets are off to their best start since the 1998-99 season, when they began 10-0.
Toledo shot 51.8 percent from the field and made 34 of 36 free throws. Drummond was a perfect 9-of-9 from the free throw line.
Pablo Bertone led Florida Atlantic with 29 points. It was the Owls' sixth consecutive loss.