Moore, the winningest starting quarterback in college football history, was nearly flawless and the Broncos' defense had no problem bottling up the punchless Lobos.
The victory gives the Broncos (11-1, 6-1) their second straight season with a single loss and looks to clear the way for another trip to the MAACO Bowl in Las Vegas, where they dismantled No. 20 Utah a year ago 26-3.
Boise State's only loss came Nov. 12 against TCU.
But Saturday was clearly a landmark day for Moore.
In his final regular season game at Bronco Stadium, the lefty was 28 of 33 for 313 yards. As usual he spread the ball around, hitting 10 different receivers, and flawlessly ran Boise State's no-huddle offense through the first three quarters.
His three touchdown passes in the game gave him 41 on the season, breaking his own previous record of 39 set in his sophomore year. He also set a new school mark for completions in a season with 300, third most all-time in the Mountain West Conference.
It was also Moore's 49th career win as a starting quarterback, the best in FBS. He also has 137 career touchdown passes, second best behind Houston's Case Keenum.
The Broncos (11-1, 6-1) sprinted to the lead, scoring three touchdowns in the first quarter thanks to Moore's accuracy - he completed 10 straight passes during one stretch - and a Broncos defense that held the Lobos to one first down in their first three possessions.
Boise State started its third possession on the New Mexico 36, and five plays later Martin scored on a 4-yard run to stretch the lead to 21-0 with 1:35 left in the first quarter.
Boise State then worked on putting the game out of reach before halftime. Midway through the second, Moore engineered an 11-play, 89-yard drive that ended with a 15-yard TD to tight end Gabe Linehan. Minutes later, Michael Frisinia tacked on a 30-yard field goal to put the Broncos up 31-0 at the half.
Moore and other members of his recruiting class are a victory away from being the winningest senior class in school history. The 2006 group, the first batch signed by Boise State coach Chris Petersen, won a second BCS bowl, forced wholesale rewrites of the school record books and elevated Boise State's national profile from a pest from a small conference to a program that proved it could consistently beat teams from college football's biggest and best leagues.
As for the Lobos (1-11, 1-6), they are at the other end of the college football spectrum. They have lost 22 straight road games, the nation's longest such skid.
New Mexico had 197 total yards and crossed midfield only twice against the Broncos.
The loss gives the Lobos three straight seasons with just one win and closes out the brief, seven-game tenure of interim coach George Barlow, who took over in September after Mike Locksley was fired.
But Saturday's blowout in Boise also ushers in the Bob Davie era in Albuquerque. The former Notre Dame coach and television analyst will take over head coaching duties this month.
B.R. Holbrook was 16 of 28 for 145 yards and was sacked twice for New Mexico.
The Broncos scored once in the third quarter when Martin dashed 40 yards down the left sideline to put Boise State up 38-0.
Moments later, Moore, Martin and many other Broncos seniors walked off Bronco Stadium's quirky blue turf for the last time, closing out careers that spanned one of the most successful eras in school history.