My favorite is a little different because it wasn't a game wining series, but in Peyton Manning's senior year South Carolina came to Neyland with the idea that they were going to rough up Peyton to make him uncomfortable, a lot of late hits and shoves early on. They hit him really late on a couple of plays in a row with no flag from the refs. We noticed that Leonard Little and Al Wilson just started losing it (at that time the Vols bench was just in front of us on the East sidelines), having to be restrained by coaches as they went out on the field yelling at refs. They were like rabid dogs. Helmets off. Total fury. South Carolina goes out on offense and two plays later they are carrying the SC quarterback (Anthony Wright, I think) off the field with a broken leg after two consecutive hits by Little and Wilson. There weren't any other late hits on Manning in that game.
The Stoerner fumble wasn't a great series but it was a fantastic play by Billy Ratliff right in front of our seats. (Amazing how you can't find any of the 30,000 Tennessee fans who left the stadium before that play, but you can find 200,000 people who say they were there..)
The goal line stuff of Eddie George was fantastic.
The stop of LSU Heisman trophy winner Billy Cannon (who, by the way, goes on to graduate from UT Dental School after his pro career) on the goal line in an upset with national implications is legendary.
My all time favorite story, way before my time, goes back to the early days when the football field was just bleachers that seated maybe 500 and fans could stand along the sidelines. It's late in a game against Kentucky and they are about to score what would be a winning touchdown, when an old man in a long duster coat just walks out onto to the field and up to the Kentucky huddle. He opens his coat up to show a revolver stuck in his belt and informs the Kentucky players that the first man who crosses the goal line is a dead man. Kentucky fumbles on the next play and Tennessee wins. I read that story several years back in a credible article about the early days of Tennessee football. It says everything about Southern football.