The Hawks (23-9) led by eight points at halftime, but a 15-6 run early in the second half gave the Bulldogs a one-point lead with 11 minutes, 25 seconds to play.
That's when Natasha Cloud took over. The junior guard tallied nine of her 13 points down the stretch to propel St. Joseph's.
"At that point, Coach had dug into me a little bit," Cloud said. "She told me that I needed to shoot the ball, so I did it and we made plays."
Twelve of Shields' points came from behind the arc. Her fourth three-pointer of the night, which came with 9:46 left in the first half, was her 92d of the season and pushed her atop the Hawks' single-season list in that category.
"We have two very good guards," Griffin said. "Erin is very unassuming because she's 5-foot-5, but she's quicker than any kid out there and she's tougher than most kids out there. Natasha is also a fighter and they play off of each other."
Ashley Robinson had 10 points and 10 rebounds for the Hawks.
The win was St. Joseph's first in the NCAA tournament since 2000. Last season in the Storrs subregional, the Hawks fell to Vanderbilt, 60-54.
"It means a lot - it's been an unbelievable experience," Shields said. "I think being here last year, getting the loss, you know how that feels now. We were ready to come in here and show what we have."
Erika Ford led Georgia (20-12) with 16 points.