The Mountaineers (17-4) led by as many as 20 in the second half, but Admon Gilder led the Aggies on a 22-8 scoring run to bring them within six.
Carter helped his team increase the lead to 13 points with 2:36 left. Gilder once again got the Aggies within single digits and a J.C. Hampton 3-pointer with 14 seconds left brought A&M within 79-77.
Since Texas A&M (11-9) was out of timeouts, Tonny Trocha-Morelos fouled Esa Ahmad with 4.4 seconds left to preserve time. Ahmad, who was 4 for 10 at the line at that point, made both free throws to give West Virginia a four-point lead.
Gilder led the Aggies with 24 points. Tyler Davis had an impressive game for the Aggies with 19 points and 18 rebounds.