Baker hit six 3-pointers, also a career best, and had five assists for New Mexico State (6-5), which snapped a three-game skid. Pascal Siakam had 14 points and 10 rebounds while Jalyn Pennie scored a career-high 14 with eight boards. Matt Taylor added nine points and a career-best eight assists.
The Aggies took a 31-30 lead into halftime and led 38-37 before back-to-back 3s by Baker sparked a 10-1 run that made it 48-38 with 13 minutes left.
Omega Harris hit a 3-pointer and Lee Moore made a layup to pull UTEP (6-4) within five about 90 seconds later, but Baker scored 10 and Siakam eight as New Mexico outscored the Miners 25-10 over the final 11 minutes.
Harris led UTEP with a career-high 23 points.