"We showed it's going to be some ups and downs this year," Tuberville said. "We're going to have a lot of growing pains. But when you win with growing pains, that means you're doing something right."
Tuberville took over after the popular and successful Mike Leach was fired in December amid allegations he mistreated an injured player.
Potts was 34 for 53 with no interceptions and connected with Lyle Leong for three scores and Detron Lewis for the other.
The pace of the offense is much quicker -- lots of no-huddles -- this season, and Potts likes it.
"There's no lollygagging around and playing backyard football out there," he said. "Everything's got a purpose, everything's detailed."
Texas Tech ran its winning streak against SMU to 14 games, dating to 1989.
Eric Stephens rushed for a 3-yard TD to put Texas Tech up 35-14 midway through the third quarter.
The Mustangs had a chance late and were driving when they failed to convert a fourth-and-21 from the 50 on their final drive.
Texas Tech intercepted SMU quarterback Kyle Padron three times. He threw for 218 yards.
SMU coach June Jones said he was "a little disappointed" in Padron, who he said got rattled.
"You can't turn the ball over," Jones said. "He's got to play through those things."
The Mustangs rallied behind their special teams. Darryl Fields returned a kickoff 92 yards to set up a 24-yard field to pull SMU to 35-17. Early in the fourth, Matt Szymanski booted a 61-yard field goal, his longest ever.
The Mustangs also blocked two field goals.
SMU pulled to 35-27 midway through the fourth quarter after taking over on downs on the Tech 32.
On fourth-and-six from the 13, Padron threw into the end zone and it looked like safety Cody Davis had broken it up. But the ball stayed up in the air and Cole Beasley caught it for a score.
Texas Tech's defense had the task of trying to stop Padron, who threw for a school-record 460 yards and two touchdowns running coach June Jones' run-n-shoot in a 45-10 win over Nevada in the Hawaii Bowl.
"The biggest question we had is our youth in the secondary, but I think they came out and responded," defensive coordinator James Willis said. "They didn't take this team lightly."
For Leong it was a career day in receptions and yardage, grabbing 11 passes for 142 yards.
"He's a great receiver," said Potts, who played with Leong since the two were in grade school. "He's great with his hands. He doesn't drop many."
Stephens' touchdown came late in the third quarter when he juked back and forth in the backfield before getting around defenders on the right side and skipping untouched into the end zone.
Tech's special teams and defense set up the first two Red Raiders scores. Cornelius Douglas forced a fumble as Kenneth Acker fielded a punt deep in SMU's own territory late in the first quarter and Franklin Mitchell recovered it at the 18.
Tech ran the ball four consecutive times -- something Leach rarely did -- before Potts found Leong in the corner of the end zone for a 2-yard touchdown to give Tech a 7-0 lead.
On the second play of SMU's next possession, redshirt freshman Jarvis Phillips stepped in front of a pass from Padron to set up Potts's second TD pass. The 6-yard score went over the middle to Leong, who was wide open near the back of the end zone.
SMU scored its first touchdown on its final drive of the first half as Padron led a 13-play drive, including his scrambling for 18 yards for a first down on fourth-and-3 from Tech's 34. Zach Line scored from 2 yards and the Mustangs were down by only one score.
Tuberville's 111th career victory came in the Red Raiders now-less-lopsided stadium. The east side of the stadium now has a $25 million addition where all 29 new suites were sold for the opener. The addition ups the stadium's capacity to 60,454.
In two weeks, Texas Tech hosts No. 5 Texas -- a huge Big 12 test for Tuberville.
"It's good we have another game on the road before we jump into the Big 12," he said. "We're not a great team right now ... execution has got to get a lot better."