Georgia (3-0) also got 15 points from Gerald Robinson and 14 from freshman Kentavious Caldwell-Pope.
Nate Wolters scored 15 to lead the Jackrabbits, and Taevaunn Prince added 13.
The two teams opened the game with atrocious offense. The Bulldogs made just three of their first 18 shots, and the Jackrabbits just two of their first 10.
South Dakota State was first to put together some offensive consistency with an 8-0 run that gave the Jackrabbits a 17-10 lead with 7:11 to go in the half. Wolters, averaging 26 points a game coming into the contest, scored his first five points during the stretch.
Robinson shouldered Georgia's first-half rally, scoring seven straight points that tied the score 22-22 with 3:04 left in the half. It was tied 29-29 at halftime after Prince's putback at the buzzer.
By then the two teams had warmed up to a relatively efficient 35 percent from the field.
The Jackrabbits raced to an early lead in the second half, going up 38-31 with 17:08 remaining on a layup by Chad White. But the Bulldogs rallied with a 7-0 run, capped by Robinson's steal and layup that tied the game 38-38 with 15:45 to go.
Georgia took its first lead of the second half on a 3-pointer by Caldwell-Pope with 14:09 remaining. At 10:20, Caldwell-Pope tipped in a basket to put the Bulldogs up 52-44.
South Dakota State hung in until Georgia's athleticism led to three straight baskets by Djurisic, on a lob, a fast-break layup and an acrobatic layup, giving Georgia a 66-55 lead with 3:36 to go.
South Dakota State never warmed up from the line, hitting just 12 of 23 free throws (52.2 percent).