The Lobos (0-5) got their only first-half score off Potts' second interception. Donovan Porterie threw a 7-yard TD pass to Josh Fussell in the second quarter.
Porterie completed 30 of 56 passes for 316 yards and two touchdowns.
The loss for New Mexico was its ninth straight dating to last season.
The game capped a week of off-the-field distractions for both teams.
Red Raiders coach Mike Leach made headlines when he indefinitely suspended Brandon Carter, a team captain and preseason All-America pick, for violating team rules following Texas Tech's 29-28 loss to No. 12 Houston. Carter was in the stands for much of the game. He did not practice with the team this week.
Leach also banned his players from using Twitter after learning Marlon Williams had tweeted about Leach being late to a team meeting.
For the Lobos, coach Mike Locksley is under investigation by the university following a Sept. 20 fight involving an assistant. Receivers coach J.B. Gerald told police Locksley struck him during a staff meeting. Gerald hasn't been with the team since the incident.
At the outset, Texas Tech showed no signs of being distracted.
On its first possession, Potts threw a 79-yard pass to Tramain Swindall, who outran Lobos defenders to the 1 on the Red Raiders' longest play from scrimmage this season. Jeffers took the ball in on the next play to put the Texas Tech up 7-0.
Potts, who was without a touchdown pass, was not on the sideline after halftime. He got sacked hard twice late in the second quarter.
Tech trainers checked Potts' balance -- he stood on one foot and then the other -- and rubbed the back of his neck.
Lobos linebacker Carmen Messina sacked Potts on a first-down play and Johnathan Rainey threw him to the ground on third-and-9 after Potts scrambled toward the far sideline late in the second quarter.
The nation's leading passer got up slowly after the second sack, then stood still momentarily as he bent over, resting his hands on his knees. His head was down as he made his way to Texas Tech's sideline.
Sheffield replaced Potts and led the Red Raiders on an 86-yard drive to a touchdown, finding Torres on a 25-yard score with 1 second remaining in the half for a 14-7 lead.