Doege threw touchdown passes of 20, 39, 7, 12, 11 and 14 yards and completed 27 of 35 passes before being replaced by backup Michael Brewer early in the third quarter.
Eric Ward caught three of Doege's touchdown passes and Jace Amaro got two of them as the senior quarterback made it look easy for Texas Tech (3-0).
The Red Raiders finished with 702 total yards, 325 on the ground.
New Mexico (1-2) struggled on offense and alternated starter B.R. Holbrook and backup Cole Gautsche at quarterback throughout the game. The Lobos finished with just 127 yards of offense.
The lone bright spot for New Mexico, shut out in the second half, came when Chase Clayton returned a kickoff 98 yards for a touchdown to pull the Lobos within 28-14.
Doege, who is in his second year as starter, became the ninth Red Raiders quarterback to pass for 5,000 yards when he found Bradley Marquez for an 18-yard completion in the first quarter. He got his 500th completion, the seventh Texas Tech quarterback to do so, when Marquez caught a 4-yard pass from him in the second quarter.
Eric Stephens lead Texas Tech's rushers with 118 yards on 12 carries and Kenny Williams had 105 yards on 14 carries.
Texas Tech's defense, long a weakness, showed why it was in the top 10 nationally coming into the game. The Red Raiders contained the pistol option the Lobos tried to use to keep Texas Tech's potent offense off the field.
Only once did New Mexico consume substantial time off the clock. The Lobos had a 17-play drive that took 7:41 bridging the first and second quarters and led to their first score when Demarcus Rogers ran for a 2-yard TD to make it 14-7.
It was the Lobos' first score in five quarters after they were shut out by Texas 45-0 last week, but it showed how they hoped to slow the Red Raiders' offense.
Doege was sharp all night. On the drive that led to his third touchdown pass to Ward that made it 28-7, he completed 7 of 8 passes during an 11-play drive.
Clayton muted most of the 58,955 Red Raiders fans on the next play when he took the kickoff and went nearly untouched along the sideline for a touchdown. It was Clayton's second kickoff return for a touchdown this season. He got the first one, also for 98 yards, in the season opener during a 66-21 win over Southern.
New Mexico's offense sputtered early, crossing into Texas Tech territory only once in the first quarter. Early in that drive Holbrook, who started the game, went out and Gautsche came in and together they took the Lobos down the field.
Lobos coach Bob Davie earlier this week said Holbrook was doubtful and his injured ribs were very sore.