"The big difference all the way around was the kicking game," said Majors, who got his 100th victory at Tennessee in his 14th season.
"At halftime I was very disappointed because they had won the kicking game going away, but we started the second half with an electrifying return by Dale Carter. Carter was a big factor."
No. 14 Tennessee, 7-2-2 overall and 4-1-1 in the Southeastern Conference, got a school-record five touchdown passes from Andy Kelly, three to Carl Pickens, to gain the inside track for a share of the SEC title and a berth in the Sugar Bowl on Jan. 1.
The Volunteers play Vanderbilt Saturday, with a victory worth at least a share of the league title.
Kentucky finished 4-7, 3-4 in its first season under Coach Bill Curry.
"The obvious key to the game was the play of Dale Carter," Curry said.
Carter sparked the Volunteers to 21 third-quarter points. He returned the second-half kickoff 69 yards to set up one score, returned a punt 29 yards to set up another, and scored himself with a 41-yard interception return.
Kelly and Pickens had scoring pass plays of 71, 12 and 25 yards. Pickens caught 10 passes for 201 yards and tied a 44-year-old school touchdown reception record.
Kelly also connected for touchdowns of 22 yards to Anthony Morgan and 12 yards to Alvin Harper. Kelly completed 19 of 32 passes for 300 yards.
Carter's interception return made it, 35-21, but Kentucky cut it to, 35-28, on a four-yard,fourth-down pass from Ryan Hockman to Phil Logan with 7:37 to play.
The Volunteers came back to drive 68 yards in seven plays, five of them passes to Pickens, who eluded two tacklers and scored from 25 yards out for the final points.
Tony Thompson gained 79 yards in 22 carries for Tennessee, giving the reserve tailback 1,025 yards since taking over for the injured Chuck Webb.