The Red Raiders fell behind early but rallied and held the Bobcats scoreless after the first quarter.
Doege, who played most of the game, went 23 for 33. He threw two touchdown passes for 20 yards and one for 10.
Eric Stephens ran for two touchdowns - one a 46-yarder where he went untouched up the middle to put the Red Raiders up 23-10. He finished with 118 yards on 21 carries.
Darrin Moore, Doege's favorite target, caught 12 passes for 221 yards.
The Bobcats (0-1) started off solid with an option-type ground game that gave Texas Tech's defense fits. Three of the Bobcats' four fumbles, by quarterback Shaun Rutherford and running backs Marcus Curry and Terrence Franks, led to touchdowns for the Red Raiders (0-1).
Once Texas Tech's offense got on track they moved easily down the field, mixing its pass-heavy offense with the run. The Red Raiders actually ran more than they passed but got more yards in the air. Texas Tech got 157 yards on 33 carries.
The Red Raiders didn't give up a lot of points but the Bobcats chewed up yardage on the ground. Rutherford, who had 82 yards on 12 carries and used Curry, Franks and Tim Hawkins out of the backfield, appeared to flummox the Red Raiders.
Texas Tech gave up 256 yards on 50 rushes by the Bobcats. That's more yardage than they gave up on the ground last season (162 yards per game).
Texas State moved the ball easily on the ground in the first quarter and built a 10-0 lead. The Bobcats also got help with sloppy tackling by Texas Tech.
Texas State got a 40-yard field goal on its first drive and then got the ball right back. Matt Harris forced a fumble after Darrin Moore caught a 5-yard pass from Doege.
Darryl Morris recovered the ball on Texas Tech's 41. Texas State kept in on the ground and Marcus Curry scored on a 7-yard run to go up 10-0.
The Red Raiders got a break when Will Johnson kicked the ball out of bounds, giving Texas Tech the ball its own 40. Two plays later, Doege found Moore along the near sideline and he pulled in a 41-yarder over his shoulder and down to the Bobcats 10.
The junior quarterback hit Brad Marquez on a fade pass in the corner of the end zone to trail 10-7 late in the first quarter.
The Bobcats got pinned at their own 1 on the kickoff when Isaiah Bell and Derek Lopez collided on the kickoff. That field position wasn't what hurt Texas State, though.
On the next play quarterback Shaun Rutherford threw the ball out of bounds, but he hadn't left the pocket and was still in the end zone, which gave Texas Tech a safety and a 10-9 deficit going into the second quarter.