Dustin Ware scored 10 for Georgia (15-17), which had upset Mississippi State a night earlier but could not sustain the momentum against the Commodores for more than a half.
Georgia led 25-24 at halftime, but missed 21 of 27 shots in the second half.
Tinsley scored the first five points of the second half for the Commodores, who soon after built a double-digit lead that grew as large as 22 points.