It was Kentucky's first win over Auburn since 1966.
Cobb set up the winning score with a 61-yard zig-zagging run two plays earlier. Cobb rushed 12 times for 109 yards mostly on direct snaps from the Wildcats' wildcat and Derrick Locke ran 19 times for 137 yards.
Kentucky (3-3, 1-3 Southeastern Conference) had tied the score with 6:29 to play on a 2-yard run by quarterback Will Fidler. Fidler came off the bench in the second half to lead the comeback. He replaced freshman Morgan Newton, who had started the game in the place of injured Mike Hartline.
Auburn (5-2, 2-2) held a 14-7 halftime lead, but was held scoreless by the Kentucky defense in the second half. Ben Tate rushed 31 times for 132 yards, his fifth 100-yard game of the season.
Auburn had one last chance to tie the game as the Tigers drove from their own 20 into Kentucky territory. The drive started with a 10-yard keeper by quarterback Chris Todd and an 18-yard run by Tate. But the drive was thwarted by two false start penalties and ended with 1:36 to play on fourth-and-11 from the Auburn 48 when Chris Todd's pass to Terrell Zachery fell incomplete.
Both teams were ineffective passing the ball on a cold night. Kentucky gained only 75 yards in the air, while Auburn had 95 passing yards.
Defenses mostly dominated in the first half. Auburn's Jake Ricks blocked Lones Seiber's 38-yard field goal attempt in the first quarter and Neiko Thorpe scooped it up and raced 69 yards for a touchdown.
It was the first score on a blocked field goal attempt for the Tigers since 1981, when Chris Martin returned a blocked kick 77 yards for a score against Georgia Tech.
Making his first start at quarterback, Newton was shaky at first, overthowing receivers and appeared to be nervous. But he started to warm up in the second quarter and scored on a 4-yard run with 9:02 to play in the half. Kentucky's score came after a six-play, 53-yard drive that included a 23-yard sideline pass to Chris Matthews.
The game remained tied until Auburn took advantage of a poor Kentucky punt and got the ball at the Kentucky 48 at 5:26 in the half. The Tigers then took control of the ball, driving methodically to Tate's 1-yard touchdown run with 6 seconds to play in the half.