Earvin Morris had given UTEP (5-0) a 69-63 lead with a layup at 42 seconds left, and Vint added two free throws with 18 seconds left to ice the win.
Southern Illinois (5-1) was paced by a career-high 25 points from Sean O'Brien, who also blocked three shots. Mike Rodriguez added 10 points.
The game was tense throughout, with 10 ties and 13 lead changes. SIU's largest lead was five points in the first half, and UTEP's largest was nine points midway through the second half.
The Miners shot 43 percent (22 of 51), and while the Salukis shot 41 percent (26 of 64), they made just 5 of 22 3-point tries. UTEP outrebounded the Salukis 37-33.
