Georgia stretched its lead to 54-41 on Robinson's layup with 8:12 remaining, but Mississippi State had one last rally. Jalen Steele scored nine points in 90 seconds, and his final 3-pointer pulled the Bulldogs within 60-57 with 3:44 remaining.
But Georgia (15-16) - the tournament's No. 11 seed - held on for the surprising win. Robinson's jumper with 59 seconds left gave his team an insurmountable 66-59 lead.
MSU's Arnett Moultrie had a SEC-best 18 double-doubles this season, but finished with just seven points and eight rebounds.
Mississippi State has lost six of its past eight. Georgia has won three of four and will face Vanderbilt in the quarterfinals on Friday.
Georgia had already beaten Mississippi State once this season -- a 70-68 overtime decision in Starkville – and it started a downhill spiral that included a five-game losing streak and tumble from the national rankings. And the Bulldogs were a handful for Mississippi State once again.
Mississippi State's NCAA tournament resume took a major hit with the loss. Missing the "Big Dance" would be a crushing blow for a team that was ranked No. 15 in the nation just a month ago, but fell apart in February and March.
Georgia has struggled for much of the season, but improved during February. The Bulldogs came into the tournament after winning two of their final three regular-season games, including an impressive 76-62 victory over Florida.
Georgia last won the SEC tournament with a miracle run in 2008, winning four games in four days after finishing 4-12 in league play.
Early, it didn't look good for Georgia.
Mississippi State controlled the opening minutes and a powerful, two-handed Wendell Lewis jam in traffic gave the Bulldogs an early 14-7 lead.
But Georgia recovered and stayed close before taking a 29-27 lead on Nemanja Djurisic's long 3-pointer with 1:03 remaining. Georgia led 31-29 at halftime and then cruised in the second half, shooting 51 percent from the field in the final 20 minutes.
Djurisic scored 11 points and grabbed 11 rebounds.