The Ospreys shot 50 percent (30 of 60) from the field and 42.9 percent (9 of 21) from beyond the arc. Smith led the offensive charge, draining six 3-pointers in 11 attempts.
BaeBae Daniels had five of the Ospreys' nine blocks.
North Florida carried a 40-36 advantage into halftime and opened the second half with a 9-2 scoring run as the Ospreys outscored the Tigers 39-29 in the final 20 minutes.
North Florida had lost each of its past six season openers.
Edward Waters (1-2) committed 21 turnovers and made just 11 of 32 shots in the second half. The Tigers were outscored off the bench 48-10, including a 32-2 discrepancy in the second half.
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.