Augustus, a backup averaging 5.4 points a game, was 6 of 9 from the field and 3 of 4 from 3-point range - a surprising hot streak for a guy who came into the tournament shooting just 22 percent (4 of 18) from behind the arc this season.
He helped MSU (20-12) advance to play South Carolina on Friday. Coach Rick Stansbury's team also kept alive its chances of making the NCAA tournament.
Georgia (12-20) had hoped for another run through the tournament. The Bulldogs stunned everyone by winning four games in three days in Atlanta last year and claimed an automatic NCAA bid.
Terrance Woodbury led Georgia with 14 points and seven rebounds.
MSU, which leads the league in 3-pointers made, used some key ones to open up a huge lead in the first half and then pull away after the break.
MSU used a 16-2 run midway through the opening half to turn a tight game into double-digit lead.
Augustus got it started with consecutive 3-pointers, Varnado made a couple of shots in the paint and Riley Benock hit a jumper that made MSU look much more like the team that started 6-2 in conference play rather than the one that lost five of its next six.
Ravern Johnson sank a free throw, then prompted a timeout with his third 3-pointer of the half with 5:51 left. MSU was up 30-17 at that point and extended the lead to 14 with Brian Johnson's rebound and dunk just before the buzzer.
Georgia sliced into the 40-26 halftime lead by outscoring MSU 13-5 to open the second half, but MSU pulled away with more 3s. Barry Stewart and Augustus made back-to-back shots from behind the arc, then Stewart added another one a few seconds later that made it 60-44 with 12:13 to play.
MSU finished 9 of 24 from 3-point range.
Georgia wilted down the stretch, no surprise for a team that's spent much of this season in turmoil. Coach Dennis Felton was fired in late January after Georgia started 0-5 in league play. Interim coach Pete Herrmann took over, but the losses kept mounting.
Georgia won three of its final six heading into the tournament, giving players confidence they might be able to pull off another improbable run to the NCAA tournament.
MSU didn't let it happen.
Ravern Johnson, the team's top 3-point threat, had a quiet game. He was 3 of 10 from behind the arc and finished with 12 points. No worries, though, Augustus picked up the slack.