Yeldon ran the ball 15 times for 72 yards and McCarron completed 19-of-28 passes for 275 yards for the Crimson Tide (8-0, 5-0 SEC), who rolled to an 11th consecutive victory.
Kevin Norwood made six catches for 112 yards and a touchdown and Amari Cooper made a 54-yard TD catch on the third play of the game.
The Volunteers (4-4, 1-3), who knocked off a ranked opponent last week with a win over South Carolina, converting just three of their 12 third-down chances.
Justin Worley was limited to 8-of-15 through the air for 120 yards. He tossed two interceptions, including one that Landon Collins returned for a touchdown.