Jerrold Brooks led the Golden Eagles (2-0) with 17 points, and Davis added 14. Southern Miss won its season-opener in overtime as well, beating Western Kentucky 67-64.
Georgia scored the first basket of the game on Vincent Williams' 3-pointer, but the Golden Eagles scored the next 15 points, capped by Neil Watson's breakaway layup. Southern Miss held the lead until the last 82 seconds.
With just over two minutes remaining in regulation, Georgia trailed 55-50 when the shot-clock buzzer sounded erroneously, stopping play. On the inbounds play, Djurisic hit his second 3-pointer. At 1:49, he tied the game 55-55 with a short jumper. Those were the last points of regulation.
In overtime, Marcus Thornton's follow-up at 4:38 gave Georgia a 57-55 lead, its first since early in the game.
The teams traded 3s before Southern Miss' Davis hit a pair of free throws with 2:01 left. Georgia was on the verge of a shot-clock violation when Craig stole the ball near midcourt and fed Davis for the game-winner.
During the Golden Eagles' 15-0 run, the clock froze at 12:36. Play continued, and the clock was restarted without stopping play. But when play stopped at 12:11, officials consulted with the timer and reset the clock to 12:36 and resumed play.
In the first half, the Southern Miss zone sealed off the inside. Georgia played nearly 16 minutes before freshman reserve Brandon Morris scored the Bulldogs' first two-point field goal on a follow-up with 4:22 remaining. That cut Southern Miss's lead to 26-17.
Georgia cut the halftime deficit to 31-27 when Sherrard Brantley hit a 40-foot buzzer beater.
Georgia had an opportunity to cut the gap to one point early in the second half when Djurisic went to the line to convert a three-point play. He missed his free throw, leaving the score 31-29. The Golden Eagles reeled off seven straight points to go up 38-31 on Rashard McGill's back-door layup with 17:08 to go.
The Bulldogs missed consecutive 3-point shots by Djurisic and Caldwell-Pope to tie the game at 45-all inside of nine minutes, before Michael Craig converted a loose ball into a layup that put the Eagles ahead 47-42 with 8:02 to go in the game.
Djurisic hit two free throws with 6:48 showing to cut Southern Miss' lead to 47-46, and after Jerrold Brooks nailed a 3-pointer to beat the shot clock for the Golden Eagles, Djurisic answered with another 3 of his own. Brooks merely came back with another 3-pointer, putting Southern Miss ahead 53-49.
Brooks jammed his 3-point attempt for the Eagles between the rim and the backboard, giving Georgia the ball with 57 seconds to go.
The Golden Eagles forced a long 3-point airball by Caldwell-Pope, and a shot-clock violation gave the ball to Southern Miss with 22 seconds to play.
The Eagles called two timeouts with 13.1 seconds to go to set up their last shot. But Caldwell-Pope intercepted Jonathan Mills' pass with 1.8 seconds remaining in regulation. Georgia could not get a shot up.