The Anteaters (5-11) pulled within 63-60 with 20 seconds left on Eyassu Worku’s 3-point shot.
But A.J. Harris’ layup with nine seconds to go, sealed it for New Mexico State (12-3).
Lofton, who was 6-of-8 from the free throw line in the final two minutes, also added eight rebounds, while Jones contributed four assists.
Sidy N’Dir delivered 13 points, while Eli Chuha had 12 for New Mexico State.
Worku led UC Irvine with 19 points.
New Mexico State jumped to an 18-5 lead on a Chuha layup with 13:18 left in the first half.
But the Anteaters responded and trailed only 20-14 after a Worku 3-pointer with 7:01 left in the half.
The victory caps a nine-game road trip that included a 63-54 win over then-No. 6 Miami that was the Hurricanes first loss of the season. It was the Aggies first win over a ranked opponent since 2007.