Both teams opened their Southeastern Conference campaign and Georgia did so with an unexpected road win that featured a strong showing down the stretch of the extra period.
Missouri took a 63-58 lead with 2:51 to go in overtime thanks to a 3-point play by Earnest Ross, but it was all Georgia after that.
Djurisic hit a layup and then made a 3-pointer to tie the game and the Bulldogs went in front for good at 65-63 with 37 seconds left on a layup by Charlie Mann.
Mann led the Bulldogs (7-6) with 18 points and seven rebounds. Djurisic added 16 points while Kenny Gaines had 11 and Brandon Morris chipped in 10.
Jabari Brown scored 19 for Missouri (12-2). The Tigers' only other setback was a one-point loss to Illinois on Dec. 21.
Missouri forced the overtime thanks to a 3-pointer by Jordan Clarkson with 55 seconds to go in regulation.