Mississippi State led by 19 at 30-11 midway through the first half, but McPhee, a walk-on, made three 3-pointers in the first nine minutes of the second half to cut the lead to 47-43.
McPhee, who had a career-high 15 points, added another 3 with 7:11 remaining to cut State's lead to 52-50, but the visitors scored the next eight points.
Georgia freshman Dustin Ware had 14 points, including a 3-pointer with 19.7 seconds left cut Mississippi State's lead to 64-61.
Ravern Johnson led Mississippi State (14-6 overall, 4-1 Southeastern Conference) with 21 points, all in the first half.
Georgia (9-10, 0-4) has lost six straight.