Behanan's shot with 1:04 remaining put the Cardinals (30-9) ahead for good, capping a rally that saw them storm back from an 11-point, second-half deficit.
Louisville's Russ Smith (19 points) hit two foul shots for a three-point advantage with 16 seconds left and the fourth-seeded Cardinals hung on after Bradley Beal and Erving Walker each missed 3-point tries for the Gators.
Louisville now goes to New Orleans where it will play the winner of the Kentucky-Baylor quarterfinal in one national semifinal.
Beal and Erik Murphy each netted 14 points for seventh-seeded Florida (26-11), which went 0-for-9 from beyond the arc in the second half.
Interpol investigating stolen passports on missing flight
Senate Democrats to pull all-nighter on climate change