Potts threw completed 32 of 46 passes with an interception for the Red Raiders (7-5).
Texas Tech kept the Cougars (5-7) from becoming bowl eligible and avenged a 1-point defeat at Houston last season.
Houston moved the ball well between the 20-yard lines, but couldn't get it across the goal line enough.
The Cougars pulled within 28-20 on a 13-yard pass from David Piland to Tyron Carrier early in the fourth quarter. But Texas Tech came right back, as Potts threw a 19-yard touchdown pass to Lyle Leong to cap a 92-yard drive.
Piland, a true freshman, completed 32 of 61 passes for 441 yards, two touchdowns and three interceptions.
Houston is now 8-6 against the Red Raiders in Lubbock. Last year, Cougars quarterback Case Keenum scored on a 4-yard run with 49 seconds left to beat Texas Tech, 29-28.
The Cougars outgained the Red Raiders 585-488, but Texas Tech made more of their yards.
Potts surpassed the 3,000-yard passing mark for the season in the first quarter. Texas Tech, predominantly a passing team under former coach Mike Leach, now has had a quarterback pass for 3,000 yards in 11 straight seasons.
In the third quarter, Potts faked to running back Baron Batch and kept it for a 28-yard rush to put the Red Raiders at the 16-yard line. Two plays later, Potts found Batch on a screen pass, and he battled through two tacklers before getting into the end zone for an 8-yard touchdown to make it 28-13.
Potts found Lewis for two touchdowns in the first half. The pair connected for a 6-yard score on the Red Raiders' first possession of the game. The second touchdown pass to Lewis -- a 9-yarder -- came at the end of Texas Tech's first drive of the second quarter to give it a 21-10 lead.
The score came after Tech got great field position on the Houston 47 after Houston punter Richie Leone's failure to get a first down on a fake punt on fourth-and-9.
After the teams traded interceptions on successive plays in the first quarter, Houston drove to Piland's 7-yard TD pass to Johnson that put the Cougars up 10-7.
Running back Eric Stephens put Tech back in front 14-10 on a 26-yard score with 1:13 left in the first quarter.