The Volunteers, who clinched a berth in the Southeastern Conference championship game last week, avoided embarrassment with a fourth-quarter comeback after trailing nearly the entire game.
Kentucky (2-9, 1-7) nearly snapped a 20-game losing streak to Tennessee, while the Vols' defense had another lackluster effort in its regular-season finale.
Down 31-22, the Vols (9-2, 7-1) scored twice in the fourth quarter to rally in the cold rain.
A trick play set up one of the touchdowns. Rick Clausen tossed the ball to C.J. Fayton, who completed a 53-yard pass to Robert Meachem at the Kentucky 12. Tony Brown scored on a 12-yard touchdown pass from Clausen two plays later.
Clausen was intercepted on Tennessee's next possession, but Kentucky could not take advantage and had to punt.
The Vols got the ball back at their 40 with about 4 1/2 minutes left and trailing 31-29.
After Kentucky's Lonnell Dewalt blocked an extra-point kick and a field goal earlier in the game, Tennessee appeared set on not leaving it up to the kicker.
Dewalt finished the season with seven blocked kicks, a school record.
Riggs ran straight through the line on third down for the touchdown, and Cedric Houston added another run for the 2-point conversion.
Clausen, playing for injured freshmen Erik Ainge and Brent Schaeffer, was 26-of-41 for 349 yards with two touchdowns and two interceptions. Houston had 127 yards rushing on 24 carries, and Meachem had five catches for 145 yards and a touchdown.
The Vols rolled up 606 yards of total offense in Clausen's second start.
Boyd threw two touchdowns to freshman Jacob Tamme and finished 20-of-32 for 218 yards.
The Vols were looking to build up some momentum going into their rematch with No. 3 Auburn for the SEC title, and clearly the defense will have to play better next week.
The defense also struggled last week in a 38-33 win at Vanderbilt.
Kentucky was playing without its offensive coordinator Ron Hudson, who resigned on Monday, and had one of the worst offenses in the country coming into the game.
But the Wildcats controlled most of the game even with their leading receiver, Glenn Holt, injuring his hamstring in the game.
Kentucky led after the first quarter for the first time this season.
The Wildcats started to pull away after Ricky Abren returned an interception 6 yards for a touchdown at the beginning of the second quarter to make it 17-7.