The Cougars came up with their first lead in the game with the first score in overtime on a Sean Hill jumper.
But NM State senior Daniel Mullings answered with a 3-pointer from the left elbow to give the Aggies another brief lead.
CSU’s Anthony Glover got open for a jumper with 3:33 to go in the extra frame for a 61-60 Cougar lead, but it would be CSU’s last of the game.
Sophomore Ian Baker got a layup on one end of the floor to regain the lead, then blocked Glover’s layup on the other end.
On the ensuing possession, senior Remi Baker buried a top-of-the key 3-pointer with 1:20 remaining and the Aggies never looked back.
“A win on the road is always hard and we’ll take it,” said NM State coach Marvin Menzies. “We had a lull late in the half and Chicago State took advantage of it. But we came on in the overtime and I’m very pleased with the way we stepped it up.
“We withstood the blows, but I didn’t expect to get hit that many times.”
Barry led the Aggies with 16 points, while playing 43 minutes, leading four Aggies with double figures scoring.
“Remi’s three was as big as it gets,” said Menzies. “He saw it was there and has the latitude to shoot. He did and that gave us the four-point lead that fueled the rest of overtime.”
Mullings added 12 points, while Pascal Siakam posted 12 with five rebounds. Baker recorded 10 points with five assists and the block.
Senior Tshilidzi Nephawe just missed a double-double with eight points and a game-high 11 rebounds to go with a blocked shot.
Chicago State was led by Rosenberg who had 14 points with seven boards and seven assists. Glover, Hill and Josh Meier each had 13 points, as Meier also grabbed seven boards.
New Mexico State recorded its second road win of the season with the victory, ending the first half of WAC play with a one-game lead.
The Aggies face the team right behind them on Saturday, as they visit Kansas City’s Municipal Auditorium to meet UMKC.