The Volunteers (5-7, 2-6 Southeastern Conference) bounced back from their heartbreaking last-minute loss to Vanderbilt by scoring first-half touchdowns on long plays en route to their first victory since upsetting South Carolina in October. Tennessee avoided its first eight-loss season in program history and improved to 76-24-9 against the Wildcats.
After throwing five interceptions without a touchdown, freshman quarterback Dobbs hit Jason Croom for a 43-yard TD and a 7-yarder to Devrin Young.
Tailback Raijon Neal meanwhile capped his senior season with 1,124 yards by rushing for 134 on 20 carries including a 60-yard TD on the game's second play.
Kentucky (2-10, 0-8) finished winless in the SEC in back-to-back seasons for the first time since 1941-42.
Tennessee finished the season by outgaining Kentucky 417-393 for its third-highest offensive output. A defense that recorded just one sack during the losing streak dropped Wildcats quarterback Maxwell Smith five times.
Tennessee defensive end Corey Miller, who entered the game with five career sacks, had a record 4.5 to pass Reggie White, who had four against The Citadel in 1983.
Dobbs finished 14 of 23 passing for 199 yards and an interception.
Saturday marked the last time as the season finale between the schools. Kentucky will face in-state rival Louisville beginning next season with the Wildcats' border rivalry becoming their next-to-last contest.
It was also Commonwealth Stadium's final game in its current configuration before work starts soon on a two-year renovation that will add suites and a recruiting lounge while modernizing other facilities.
Wildcats rookie coach Mark Stoops might need that long to continue his upgrade of Kentucky's on-field product. His first season ended in another 2-10 finish and extended their SEC losing streak to 16 games, capped by back-to-back league losses in which the Wildcats regressed on both sides of the ball.
The Wildcats managed a second-quarter touchdown through trickery including quarterback Smith going in motion on one play and running back Dyshawn Mobley taking a direct snap from the wildcat formation on another.
Smith completed the 75-yard drive by hitting Anthony Kendrick with a 19-yard touchdown pass to bring Kentucky within 20-7. He added a 14-yard TD pass to Javess Blue in the fourth quarter.
Before that Tennessee scored three big-play touchdowns, compiling 281 first-half yards that surpassed last week's total (237) in a loss to Vanderbilt.
Tennessee got on the board on the game's second play as Neal, who entered the game 10 yards shy of 1,000 for the season, got that plus 50 more on his first carry around right end for the touchdown.
Dobbs made it 14-0 two series later by completing his first TD pass of the season. But it almost became his sixth INT as Kentucky defender Jaleel Hytchye bobbled the ball twice before it bounced to the Volunteers' Jason Croom, who held on and jogged into the end zone for the 43-yard score.
Some things held form for Dobbs as Kentucky's Ashley Lowery picked him off in the second quarter without a receiver close. The Wildcats couldn't take advantage after driving into Tennessee territory a third time, catching a break when Landon Foster's punt was downed at the 2.
Poor field position didn't faze Tennessee or Dobbs, who moved the Volunteers 98 yard and capped the drive by bursting through the middle for a 40-yard TD run.