The Green Wave struck back in the second quarter when running back J.P. Losman scored from 6 yards out to tie the score at 7-7.
Nevels, who had been replaced by Zac Dahman in first quarter after an injury, returned to start the second half.
In the third period Tulane kicker Seth Marler booted a 31-yard field goal to give the Greenies a 10-7 lead with 4:34 remaining in the third quarter.
Army responded with a field goal attempt of their own but the 27-yard attempt cruelly bounced off the goal post.
Army continued to hold off the Tulane offense with sacks and big third down plays. The Black Knights held Tulane to just 24 yards rushing in a stellar defensive performance.
Army took the lead for good when Nevels rambled in from 2-yards. The score put the Black Knights in front14-10 at the start of the fourth quarter. The Tulane coaches contested the touchdown claiming Nevels had stepped out of bounds, with no success. It was only the second time this season that the Cadets had led in the fourth.
Tulane got the ball back with 2:00 remaining and proceeded to march down the field in a similar manner as UAB had earlier in the season against Army. The Cadets gave up two costly 15-yard penalties that assisted in Tulane's efforts to pull a win out.
However, with 1:30 remaining in the contest Army's Mario Smith became the hero of the day when he intercepted a Tulane pass. Carlton Jones, who rushed for 124 yards, helped the Army offense gain a first down and run the clock out for Tulane.
Army improves to 1-9 (1-6 CUSA) with the win. The Black Knights travel to Memphis next week. Tulane falls to 6-5 (3-4 CUSA) with the loss. The Green Wave host Southern Miss next week. Tulane is fighting for a possible bowl bid.