Thompson's layup with 1 second to go was the difference-maker, after Angelo State took the lead on Tre' Bennett's 3-pointer with 5 seconds to go.
The Vaqueros (3-5) led by seven with 1:36 left, but Angelo State made four 3-pointers in the last 1:28 - three by Bennett, before Thompson won it.
Thompson was 8 of 15 from the floor, 11 of 19 from the line and made 4 of 5 from beyond the arc. He grabbed six rebounds and had six assists. Dakota Slaughter scored 18 points and Dan Kimasa added 14 for Texas-Rio Grande Valley.
Bennett paced Angelo State with 26 points with eight rebounds and Shelton Boykin added 11 points.
Thompson's 3-pointer with 1:04 left in the first helped Rio Grande Valley to a five-point lead at the break, 37-32.