Caldwell stepped in front of a quick out attempt by Andrew Allen and went 40 yards for the deciding score.
New Mexico State (3-9, 3-5 Sun Belt) opened a 14-0 lead on Allen's 76-yard pass to Jordan Bergstrom. ULM's Earnest Carrington hit Marcus Green from 49 yards to halve the deficit, and later he hooked up with DeVontae McNeal on a 74-yard touchdown pass. Louisiana-Monroe trailed 21-14 at intermission.
On the Warhawks' first second-half possession, Carrington fumbled being sacked, and Stephen Meredith returned it 9 yards to put the Aggies up two touchdowns.
Allen's 10-yard scoring strike to Bergstrom tied it again at 35, but on the next drive he was picked off by Caldwell for the winning score.