1959 (Yes, that's right!) vs LSU.
There are lots of 2nd place choices but no other 1st place choice. It was electric as the Vols defeated the #1 team in the country 14-13 including a goal line stand on a 2 point conversion. Heissman winner Billy Cannon was stuffed and the place went ballistic. You young folks don't know what a real bone-crusher really is.