Vanderbilt gained a 55-50 lead after Siakam sank two free throws, but Alex Caruso cut it to 55-52 on his foul shots for A&M.
Texas A&M (14-11, 5-7) had possession down 55-52 in the waning seconds, but Jamal Jones was called for an offensive flagrant foul with 8.1 seconds left while trying to create space for a potential game-tying 3-pointer.
Luke Kornet hit 1 of 2 free throws following the flagrant for a 56-52 lead, before Kyle Fuller sank another free throw to preserve the win.
Rod Odom sent the game into overtime at 49-49 with a long jumper before fouling out in OT.
The referees reviewed to see if Odom's shot was a 3-point winner, but the game remained tied.
Siakam's dunk had cut it to 49-47 with 9 seconds left, and Dai-Jon Parker forced a jump ball with the possession favoring Vanderbilt to set up Odom's game-tying basket.
Damion Jones had 10 points and 13 rebounds for Vanderbilt, while Siakam had 10 boards. Fuller added 12 points.
Jamal Jones led the Aggies with 17 points, including 5 of 7 from long range, to go along with 13 rebounds. Kourtney Roberson added 11 points.
Texas A&M scored the first 11 points of the game and led by 11 with 6 1/2 minutes to go.
The Aggies held their biggest lead at 44-33 on Jordan Green's 3-pointer, before Vanderbilt closed the gap late. Vanderbilt used a 7-0 run to close to 44-40 on Siakam's free throws with 1:19 left.
A&M hit 9 of 20 free throws, and missed 2 of 3 in the final minute of regulation before Jamal Jones and Shawn Smith each converted a pair with less than 30 seconds left.
A&M scored the first 10 points of the game on a pair of Roberson buckets and back-to-back 3-pointers by Antwan Space and Jamal Jones. Damian Jones broke the 10-0 spurt with a basket inside.
Texas A&M didn't score for nearly 9 minutes in the first half after Caruso's 3-pointer made it 15-5, but led 23-19 at halftime.