The Tigers (43-18) will play the winner of the Coastal-Connecticut elimination game Sunday.
Hinson's two-run homer sparked a four-run eighth inning that put the game away. Shaffer had three hits and four RBIs. David Haselden (6-1) pitched four scoreless innings in relief.
The Chanticleers (42-19) cut the deficit to 7-5 in the fifth, but a pop-up bunt double play ended a potential big inning.
Tommy La Stella homered -- his third in two games -- and had three hits for Coastal.
GEORGIA TECH 6, SOUTHERN MISSISSIPPI 2
In Atlanta, Brandon Thomas and Daniel Palka homered in a five-run second inning, Jed Bradley pitched into the eighth and Georgia Tech beat Southern Mississippi in the Atlanta Regional.
Expected to be a first-round pick in next week's major league draft, Bradley (7-3) allowed eight hits and two runs with one walk and four strikeouts in 7w innings for Georgia Tech (41-20).
Southern Miss (39-19) ended the season having scored two runs in its final 34 innings.
Palka's 11th homer, Sam Dove's RBI single and Thomas' third homer, a three-run shot, made it 5-0 in the second.
GEORGIA 7, ARKANSAS-LITTLE ROCK 3
In Corvallis, Ore., Levi Hyams led off the game with a homer and Brett DeLoach hit a three-run shot in the fifth inning to help Georgia beat Arkansas-Little Rock in an elimination game in the NCAA Corvallis Regional.
Georgia (32-31) advanced to a Sunday game against the Oregon State-Creighton loser Saturday night.
DeLoach's homer made it 5-0, but Arkansas-Little Rock (24-34) came back with three runs in the bottom of the inning -- two on Jason Houston's two-out single.
Georgia answered with two runs in the sixth to go back ahead by four runs. Both runs came with two outs, the first on a passed ball and the second on a throwing error.
Hyams was 4 for 5 and scored three runs, and Zach Cone was 2 for 4 with an RBI.
Houston was 3 for 4 for Arkansas-Little Rock.
Georgia starter Alex Wood (6-7) was the winner. Calvin Drinnen (6-7) took the loss.
NORTH CAROLINA STATE 5, GEORGIA SOUTHERN 2
In Columbia, Cory Mazzoni struck out 12 and scattered four hits over eight innings as North Carolina State stayed alive at the Columbia Regional with a victory over Georgia Southern on Saturday.
Georgia Southern (36-26) closed the season with five consecutive losses.