The Spartans led by 12 with 1:57 left, but after a Kenny Gaines three-point play, the lead just three with 21 seconds to go.
Denzel Valentine finally sealed the win with six free throws down the stretch – four coming after Georgia pulled within three – and Michigan State moved on with a 70-63 win Friday.
The No. 7 Spartans will meet the winner of No. 2 Virginia and No. 15 Belmont.
Michigan State built a big second-half lead after Georgia pulled within 39-37 on the back of a 10-0 run. The Spartans responded with a 19-8 run.
Bryn Forbes got it started for the Spartans with a midrange jumper before Branden Dawson rattled off eight straight, including two three-point plays. Forbes knocked down a corner 3-pointer and Travis Trice split two defenders for a slashing layup before Forbes capped the run with another corner 3-pointer, this time with a foul.
He knocked down the free throw to put MSU ahead 58-45. The Spartans kept the Bulldogs at a distance for much of the second half until the final two minutes.
A Dawson bank shot in between defenders and a Valentine lay in off a Dawson steal gave MSU the 64-52 lead late, but Georgia was not done and Michigan State made things interesting late once again.
Georgia’s Cameron Forte hit a pair of free throws, then stripped Trice and ran away for an opencourt dunk. J.J. Frazier blocked a Matt Costello layup attempt and Charles Mann made a layup for the Bulldogs, pulling the game to 64-58.
Mann again drove the hoop for a bucket after Colby Wollenman missed the front end of a one-and-one. He made both and Georgia was down just 64-60.
Valentine hit a pair of free throws before Gaines came down for a three-point play, as he went up and drew contact from Wollenman, hitting the free throw for a 66-63 game.
But that was as close as Georgia would get, as Valentine – who finished with a team-high 16 points – hit four more free throws to seal it.
Trice was key in the first half, as Dawson was in early foul trouble. While the senior forward was on the bench for the final 14;23 of the first half, MSU went on a 30-13 run to flip the game from trailing 9-5 to leading 35-22 at halftime.
The senior guard had 11 points and four assists – two of which went to freshman Marvin Clark, who provided solid minutes and play with Dawson on the bench.
Clark finished with six points, while Dawson came back in the second half to have 14 points and seven rebounds.
Trice finished with 15 points and Forbes had 14.