The Tigers, 12-1, will play host St. Joseph's at 3 p.m. CST on Saturday in the championship game.
Smalley hit 7-14 field goals as the Tigers played without their normal starting point guard, Whitney Boddie, who is academically ineligible.
Auburn came out cold offensively and trailed 32-30 at halftime after making just 30.3 percent of its first half shots while Davidson made 46.9 percent.
The Tigers took the lead by scoring the first six points to start the second half, but Coach Nell Fortner's team was never able to pull away for a comfortable victory.
"It wasn't the prettiest of wins, but we will take it on move on," Fortner said.
"We persevered, which is the biggest thing," the Auburn coach added. "We had a new lineup and it changes your team. It is hard to lose your point guard, which did as many things as ours did, and be the same team. We are not the same team. We are just going to have to find who we are in the next few games."
The Tigers shot better in the second half, making 57.5 from the field to finish at 41.5 percent for the game. AU made just 2-11 threes and 10-17 foul shots.
Davidson, which fell to 6-5, made 39.7 percent of its shots including 5-17 threes. The Wildcats made 4-9 free throws and had 39 rebounds, three less than the Tigers.
Auburn, which trailed by as many as eight points in the first half, forced 20 turnovers and had 14 for the game. The Tigers led by as many as nine points in the second half.
Senior guard Tamela McCorvey scored 13 points and added six assists without a turnover. Sherrell Hobbs added a dozen points for AU plus seven rebounds.
AU's leading scorer, DeWanna Bonner, hit just 4-12 field goals and scored nine points, but led all rebounders with 12.
St. Joseph's defeated the Highlanders of New Jersey Institute of Technology 68-59 in the other half of the Friday doubleheader at Alumni Hall.