The Aggies owned a 10-point lead midway through the second half, but the Tigers fought back to go in front at 68-67 on Laurence Bowers' 3-pointer with 51 seconds to go.
Missouri's Phil Pressey then stole the ball from Harris, but promptly turned it over himself with a bad pass. That gave the ball back to the Aggies with 24 seconds left and they worked it to Harris for what turned out to be his third 3-pointer of the game.
Pressey then missed a 3-point try for Missouri, which lost for the second time in five games.
Harris finished with 17 points and Elston Turner added 15 for Texas A&M (14-8, 4-5 Southeastern Conference). The Aggies had lost five of their previous six.
Missouri (16-6, 5-4) was led by 15 points from Alex Oriakhi.