Smith tossed three of touchdowns in the first half as Wyoming (3-7, 2-4 Mountain West) took a 21-7 halftime lead.
The Lobos (4-7, 1-5) closed within 21-17 midway through the third quarter, but could get no closer.
New Mexico quarterback Cole Gautsche threw his first two touchdown passes of the season and gained 150 yards on the ground.
But with a chance to put together a game-winning drive after getting the ball at their 39 with 1:40 remaining, the Lobos could only gain six yards, with Gautsche missing Jhurell Pressley out of the backfield on fourth down.
Dominic Rufran caught six passes for 116 yards and a 64-yard touchdown and Jalen Claiborne had two scoring grabs for Wyoming.
After New Mexico started the scoring on a 7-yard touchdown pass from Gautsche to Andrew Aho, Wyoming responded with three straight scores in the second quarter.
Smith hit Robert Herron on an 81-yard touchdown on the first play from scrimmage following New Mexico’s touchdown and three minutes later, Rufran went the distance.
The offenses ruled the day, with the Cowboys piling up 429 yards of offense and the Lobos 551. Neither team committed a turnover.