Young poured in all of 17 of his points in the second half and Casey Prather provided 16 points with nine rebounds as Florida (24-2, 13-0 SEC) set a school record for most consecutive overall wins and 30th in a row at home.
Scottie Wilbekin contributed 15 points for Florida, which erased a 38-30 halftime deficit and ended the game on an 8-1 run.
The Tigers (12-12, 4-9) stayed close until a series of mental mistakes in the closing minutes undermined their upset bid.
Tahj Shamsid-Deen fired in five 3-pointers en route to 17 points.
Chris Denson added 16 and KT Harrell added 15 for Auburn.