The win advances the Lobos (3-0) to the semifinals of the Charleston (S.C.) Classic where they will play Massachusetts Friday. UMass was a 96-90 winner over Nebraska is its tournament opener.
New Mexico had a large first-half lead but let it slip away, and only a long running 3-pointer by Williams as regulation time expired kept the Lobos in the game and led to the first overtime with the score 75-75.
The Alabama-Birmingham Blazers (3-1) led by as many as six in the first overtime, but Kirk got a jumper with 48 seconds to go and a 3-pointer with 2 seconds left to tie the score 86-86 and caused the second overtime.
Cleveland Thomas broke the game's final tie with a 3-pointer that put the Lobos ahead 95-92 with 43 seconds to go and New Mexico was able to hang on.
Williams finished with 29 points and Cameron Bairstow, who fouled out in regulation, had 21 points. Kirk chipped in 16 points and 11 rebounds for the Lobos.
Chad Frazier, with a strong second half, led all scorers with 34 points on 11-of-19 shooting. Rod Rucker, despite 3-of-22 shooting, had 18 points and 20 rebounds for Alabama-Birmingham.