But this season, the Vols are on the fast track to several milestones.
They are on the verge of their first outright SEC regular-season title since 1967. They need one more win to tie the school record for victories in a season. And on Monday, they got the expected news: A first-ever No. 1 ranking in the AP and coaches' polls.
The ranking came as a result of a four-point win at then-No. 1 Memphis, a win that happens to be the biggest in the history of the program.
It's bigger than beating No. 1 Kentucky in 1966.
It's bigger than beating No. 1 South Carolina in 1969.
It's bigger because it propelled Tennessee to the No. 1 spot in the nation and helped generate more positive publicity than at any time in UT's hoops history.
Yes, Ernie and Bernie graced the cover of Sports Illustrated more than 30 years ago. But that didn't get Tennessee a No. 1 ranking. And Ernie and Bernie never won an NCAA Tournament game.
This Tennessee team has yet to play in the NCAA Tournament, but the win over Memphis put UT in prime position to get a first-ever No. 1 seed, which should help in Bruce Pearl's quest to advance past the Sweet 16 for the first time in Vols' history.
That's why Tennessee has never had a bigger win in men's basketball.
It was a win very much enjoyed by a former Vol who hails from Memphis – Dane Bradshaw.
Bradshaw, who finished his UT career last season, is playing overseas at Denhelder in Holland. His team is last in the league. But his other team is No. 1 in the nation. And Bradshaw couldn't be happier.
``It was a big thrill,'' Bradshaw said. ``I've played there once before. It's an amazing place, the FedEx Forum, where the Grizzlies play. You walk down the tunnel and see the NBA banners. You kind of get a taste of the good life.''
Bradshaw, who resides six hours ahead of Eastern time, said he couldn't get the UT-Memphis game on the Internet, so his girlfriend put a webcam up to a television set and he watched the last five minutes live through her computer.
Bradshaw got a kick out of seeing his former teammate, J.P. Prince, scored 13 second-half points to spark the victory. Bradshaw recommended Prince to coach Bruce Pearl when Prince decided to transfer from Arizona.
Memphis coach John Calipari insulted Prince by calling him P.J.
``Who knows, maybe it was an honest mistake,'' Bradshaw said. ``Maybe it was something to kind of get him going. The way J.P. responded in the second half, everyone in Memphis knows his name for sure now.''
Bradshaw said he's not surprised by Prince's impact.
``The knock on J.P. for a long time was to try to get him to play at the 100 percent level the whole time,'' Bradshaw said. ``He's such a talented player that for so long, he was able to get away with relying on his talent. But if the biggest problem in your game is sometimes being questioned on how hard you play, I think Bruce Pearl can get that fixed pretty quickly.''
Bradshaw thinks UT's win will help the Vols in recruiting. But he said Memphis has had the edge on UT for years because the Tigers can boast of several players in the NBA whereas UT couldn't. The Vols now have C.J. Watson in the NBA, which, Bradshaw said, should help.
``Right now, that's where Memphis has the edge on recruits because that's the ultimate goal for any player,'' Bradshaw said. ``I think Tennessee is starting to turn the corner on that with some great individual players.''
Bradshaw thinks Pearl will not only get UT to a Final Four, but one day take it all.
``I expect them to win a national championship, and I hope it's sooner than later,'' he said. ``You see the talent he brings in. I've always said, no one is ever going to underachieve under coach Pearl.''
Bradshaw also thinks Pearl will be at Tennessee for 10 to 15 more years.
``I can see him staying,'' Bradshaw said. ``I think he'll stay until he gets the job done. … I also know he's a very ambitious man. There might be some type crazy opportunity out there. I don't know if it's the NBA. But I think that's years and years down the road.
``I don't think anybody needs to worry about the Indiana job. I think he can do everything he needs to do at Tennessee. He's brought it up to a national program. I think he'll stay for a very long time. But to say that he ends his career coaching at Tennessee, that's up in the air.''
What's not up in the air is the terrific job Pearl has done turning around UT's program.
He's one win shy of tying the single season record for most victories. He's got UT ranked No. 1 in the RPI. And he's got UT ranked No. 1 in the polls for the first time ever.
Tennessee hopes it's not a one-week-and-done trip to the top of the ladder.
To keep the ranking, UT must win at Vanderbilt (23-4) on Tuesday night, then against Kentucky in Knoxville on Sunday. The Commodores are undefeated at home this season, including a 41-point win over Kentucky. No team in the country is as drastically different as Vandy is at home vs. the road. So, the fact UT won by 20 in Knoxville last month is of little importance.
Wayne Chism, who had 18 points and 18 rebounds against Vandy earlier this season, said he thinks the Vol can put behind the Memphis win.
``It ain't gonna be too difficult,'' he said. ``We've just gotta keep our mind focused on Vanderbilt.''
Chris Lofton offered the same sentiments.
``It was a great win (at Memphis) but this one's more important because it's an SEC game,'' Lofton said.
As Tennessee tries to win its first outright SEC title in 41 years, Pearl tries to keep his team – and himself – grounded.
At the Lady Vols basketball game Sunday afternoon, women's athletic director Joan Cronan wanted to introduce Pearl to the crowd to recognize the big win over Memphis.
``We've put the Memphis game behind us,'' Pearl said.
Now there's a man who practices what he preaches.