Senior DeWanna Bonner, who scored nine points and added 12 rebounds, joined Smalley on the all-tournament team along with senior Sherell Hobbs, who had four points and three steals on Sunday.
Whitney Boddie scored eight points and added seven assists while Jordan Greenleaf added eight points for the Tigers.
Coach Nell Fortner said she was glad to get the victory, but disappointed in the team's 37.3 percent field goal shooting and noted that will be a point of emphasis this week before the Tigers return to action with a Wednesday night home game vs. North Carolina A&T.
With the Tigers up by 14 at the half and building the lead to 25 points early in the second period, Fortner was able to substitute heavily and all 11 players were in for at least seven minutes of game time.
Auburn helped its cause by turning the ball over only 10 times and making 4-9 threes and 9-11 free throws. FIU had 22 turnovers and shot 41.7 percent from the field, including 7-13 on threes and 5-9 at the foul line.
"It is important that you are always competing for something and when you get the opportunity to play a tournament and compete for a championship, it is important that you fight for that and I am pleased that we got the first one," Fortner said.
"I was pleased with the big lead that we got and I was hoping we could hang on to it, but I am trying to play some different lineups and get the young players some playing time so we had some combinations on the floor that maybe need more time, but we hung on and did a nice job there at the end."
Monika Bosilj of FIU took game high scoring honors with 32 points, but her team fell to 1-5 for the season.
"I was really pleased about our turnovers and I thought we played some really good defense at times, except on Bosilj, she just had a career night and is a fantastic shooter," Fortner added. "As far as putting the pressure on them, we did a good job by holding them to 52 points, but we needed a better offensive output."
Next on the schedule is a 6 p.m. home contest as North Carolina A&T visits Beard-Eaves Memorial Coliseum.