Trailing 23-21 late in the third quarter, Sanders nudged a 42-yard attempt wide right.
It then took Tulsa less than two minutes to score on Brewer's 1-yard touchdown to push the score to 30-21.
New Mexico's Teriyon Gipson, whose status entering the game was questionable while recovering from meniscus surgery, finished with 71 yards rushing and two touchdowns. Dameon Gamblin grabbed a game-high eight passes for 131 yards.
The Lobos did appear to have pulled within range on a 29-yard touchdown pass midway through the fourth quarter, but it was called back on an illegal motion penalty.
Penalties played a big role in the game, particularly in the first half when the Lobos picked up seven personal fouls among their nine flags, the most in coach Bob Davie's four-year tenure at New Mexico.
The Lobos finished with 14 penalties for 154 yards.
The teams traded the lead four times in the first half before Tulsa took the lead for good 30 seconds into the second quarter on a 41-yard Keevan Lucas scoring catch.
Tulsa extended the lead to 23-14 by halftime on two of Jones' field goals, but it could have been more if it weren't for a red-zone stand by the New Mexico defense that was extended on fourth down by a personal foul.
AP College Football website: www.collegefootball.ap.org