Houston's David Piland was 17 of 44 for 211 yards and a touchdown in his first start since going 2-6 as a starter in 2010 when he started in place of an injured Case Keenum.
Charles Sims rushed for 77 yards on 13 carries for Houston, which was playing its first regular season game under Tony Levine after Kevin Sumlin left for Texas A&M. Levine coached the Cougars to a win in the TicketCity Bowl over Penn State last year.
Piland started the game with three straight incompletions as the Cougars went three-and-out on its first drive.
Texas State was able to jump on Houston fast, striking for a 21-yard touchdown pass from Rutherford to Curry with 10:11 left in the first quarter, capping an 8-play, 65-yard drive that took 4:22 off the clock to make it 7-0.
Matt Hogan cut the lead to 7-3 with a 50-yard field goal with 7:58 remaining in the first quarter, but the Bobcats took just 18 seconds to answer as Curry bust up the middle for a 73-yard touchdown run to make it 14-3.
Piland found Larry McDuffey for a 64-yard touchdown pass with 3:09 remaining in the first quarter to slice the lead to 14-10.
Curry went in for a 2-yard score with 12:45 left in the second quarter to extend Texas State's lead back to 11 and added a Will Johnson 32-yard field goal 7 minutes later to make it 24-10. Johnson added a 45-yard field goal to end the first half to give the Bobcats a 27-10 halftime lead.
Hogan hit a 37-yard field goal for Houston to cut Texas State's lead to 27-13 with 6:21 remaining in the third quarter. Johnson hit a 34-yard field goal with 6:32 remaining in the game to make it 30-13.
Houston, which was ranked as high as No. 6 last season and led the nation in scoring offense, passing offense and total offense, gained 326 yards Saturday night compared to the Bobcats' 444 yards.