The Lady Vols won the regular season but had limped into Georgia without Isabelle Harrison - the good news for Tennessee is she is expected to be back for the NCAA tourney - and the impact was felt inside.
The Aggies dominated the glass, 42-31 and had 18 offensive rebounds.
"We've got to get better on the defensive end," Head coach Holly Warlick said. "That's the bottom line. We've got to get better and become a better rebounding team."
Spani had a career high 33 points on 11-13 shooting, including 5-6 from behind the arc, but she got little help on offense as guards Ariel Massengale, Kamiko Williams and Meighan Simmons combined to shoot 8-30 from the field overall and 0-6 from long range.
The Aggies will play for the tourney title against either Kentucky or Georgia.