Johnson, a senior, made 7 of 14 from 3-point range on Senior Day and Renardo Sidney added 13 points and 12 rebounds for his fourth double-double of the season.
Johnson was especially hot in the first half, hitting five 3-pointers as the Bulldogs built a 29-23 halftime lead. It continued a streak of hot shooting for the 6-foot-7 guard -- he's made 26 of 44 3-pointers in the past six games.
Augustus also added 10 rebounds and hit a tough fade-away jump shot late in the second half that helped secure the win. Dee Bost added eight points and eight assists.
Mississippi State (17-13, 9-7 Southeastern Conference) led 53-40 with 5:30 remaining, but South Carolina went on a 16-6 run to cut the lead to 59-56 with 25.6 seconds remaining.
Then Mississippi State coach Rick Stansbury was called for an ill-timed technical foul while trying to call a timeout, and Malik Cooke made two free throws to pull the Gamecocks within 59-58.
But South Carolina couldn't take advantage. Bruce Ellington missed a contested 3-pointer at the buzzer that would have won the game.
Ellington scored 15 points and Cooke added 13 to lead the Gamecocks. Sam Muldrow added 10 points and seven rebounds as South Carolina lost its fifth straight game in the series.
South Carolina (14-15, 5-11) shot 23 of 64 (35.9 percent) from the field.
Mississippi State has secured the second seed in the SEC's Western Division, earning a first-round bye in the conference tournament that begins on Thursday in Atlanta. The Bulldogs will enter with plenty of momentum, winning four of their past five.
South Carolina will be the sixth seed in the Eastern Division.