Forward Yante Maten scored a game-high 21 points and guard Teshaun Hightower scored a much-needed 13 for the 12-seeded Bulldogs (18-14), who will face No. 4 seed Kentucky Friday.
The Bulldogs missed three free throws in the closing seconds but survived when Missouri guard Kassius Robertson missed a corner 3 with two seconds remaining and time ran out.
Both teams struggled from the field with Georgia shooting 38.2 percent to Missouri's 34.4.
The Tigers (20-12) overcame a nine-point halftime deficit and caught Georgia at 39-39 less than six minutes into the second period, but the Bulldogs responded with an 8-0 run to regain momentum.
The Bulldogs were up 55-47 with less than eight minutes to go before the Tigers recovered again to close the gap to two in the closing seconds.
Sidelined by a back problem since a brief, two-minute stint in the season opener, Porter Jr. entered the game at the 17:22 mark of the first half and hit his first field-goal attempt, a layup, less than a minute later to put the Tigers up 5-0.
But he struggled for much of the rest of the half, finishing with just 5 points on 2-of-10 shooting at the break. He finished the game with 12 points as his younger brother Jontay Porter led Mizzou with 20 points.
The Tigers went out to a 10-0 lead and were up 12-3 before hitting a scoring drought that would last just over eight minutes. They were 0-of-14 from the field in that stretch and fell behind 19-12 before Porter Jr. got his second basket, a 3-pointer at the 5:35 mark of the period.
But Georgia kept working behind a solid defense and the scoring efforts of Maten and Hightower, who finished the half with 14 and 11 points, respectively to give the Bulldogs a 33-24 lead at the break.
--Field Level Media
Georgia | Missouri | |
Yante Maten 21 | Scoring | Jontay Porter 20 |
Tyree Crump 3 | Assists | Kassius Robertson 3 |
Yante Maten 10 | Rebounds | Jontay Porter 8 |
Yante Maten 7 | Free Throws Made | Jontay Porter 6 |
Tyree Crump 1 | Steals | Jordan Geist 1 |
Yante Maten 2 | Blocks | Jordan Barnett 1 |