The No. 6-ranked Volunteers turned the ball over inside the Vanderbilt 20 the first two times they had it, and Heath Shuler (10 of 19 for 131 yards and one touchdown) had his poorest passing day of the season.
But Tennessee scored on three consecutive offensive plays in the second quarter and the rout was on.
"We didn't have our best day offensively and still did really well," Fulmer said. "I really think this team is a turnover or two from being undefeated. I'm not crying. We had a great season."
The Volunteers, 9-1-1 overall and 6-1-1 in the SEC, ended the regular season with 471 points, an average of 42.8 per game, breaking the school record of 41.6 points set in 1914. The 471 points is also an SEC record, breaking the previous mark of 454 by Alabama in 1973.
Charlie Garner rushed for 151 yards and a touchdown in 16 carries against Vanderbilt. James Stewart had 91 yards rushing and three touchdowns and Nilo Silvan went 63 yards to score on a reverse.
Vanderbilt finished 4-7, 1-7.
Alabama also won 57 in a row at home from 1963-82.
Miami concluded the season with a 9-2 record and probably will play No. 19 Arizona (9-2) in the Fiesta Bowl. Memphis State finished 6-5.
Collins' touchdown pass plays covered 54 yards to Chris Jones, two yards to A.C. Tellison and 25 yards to Jonathan Harris. Collins also had a 22-yard touchdown run.
Malone rushed 10 times for 143 yards, including 60 on a touchdown run, and Calvin ran 14 times for 124 yards, including 66 on a scoring run.
Officials from the Carquest Bowl, formerly the Blockbuster Bowl, were in the press box ready to extend an invitation to LSU. But the Tigers (5-6) failed to reach the necessary six victories.
Instead, LSU ended with a fifth consecutive losing season, and Virginia will be invited to play at Miami on New Year's Day, probably against Boston College.
Arkansas finished 5-5-1.
Davis set a school record with 40 carries and gave Mississippi State (3-6-2, 2-5-2) the lead for good with a three-yard touchdown run in the first quarter.
Mississippi State, which began the season with aspirations of a school-record third consecutive bowl appearance, won for the first time in five games. Ole Miss (5-6, 3-5) lost for the fourth time in five games.
Southern 31, Grambling 13--Landry Williams caught two touchdown passes and Lindsey Scott ran for two as Southern beat Grambling in the Bayou Classic at New Orleans.
Williams scored Southern's first touchdown on a 59-yard pass play from Randall Williams, who completed 13 of 24 passes for 153 yards.
The victory leaves Southern (10-1, 7-0) unbeaten in the Southwestern Athletic Conference and gives them sole possession of the SWAC championship.
Grambling finished the season 7-4, 4-3.