Schaub completed three passes for 52 yards on Houston's opening drive, including a 22-yard strike on third down the seam to Owen Daniels to set up a field goal.
Houston's next two possessions ended in turnovers when Arian Foster fumbled and Schaub's pass was intercepted by linebacker Jason Phillips on a bad throw over the middle.
Playing without his top weapon Andre Johnson, Schaub finished 3 of 6 for 52 yards for Houston (No. 6 in the AP Pro32).
Cam Newton's night also was short and not all that productive for Carolina.
Carolina's first-team offense, which finished fifth in the NFL in scoring last year, looked out of sync from the start and struggled with blitz pickups.
The Panthers (No. 20) didn't pick up a first down until their third possession when Newton showed off his incredible scrambling ability by racing up the middle for a 15-yard gain on third down. Unlike last year when Newton would challenge would-be tacklers, he elected to slide after picking up the first down -- and looked a little awkward doing so.
That drive ended with Olindo Mare's 33-yard field goal. Newton and the rest of the Carolina starters were taken out with 4:14 left in the first quarter.
Newton finished 2 of 6 for 17 yards.
Jonathan Stewart, who signed a five-year contract extension with Carolina hours before the start of the game, didn't carry the ball and caught one pass for 13 yards. DeAngelo Williams got the start and ran four times for 13 yards.
Houston's only touchdown of the first half came on 5-foot-5 Trindon Holliday's 90-yard kickoff return in the first quarter.
Carolina's No. 2 quarterback, Derek Anderson, was 9 of 12 for 99 yards passing with one interception, but looked sharp leading the two-minute offense near the end of the first half. Anderson moved the Panthers 83 yards on eight plays, although he got some help when the Texans were flagged for three penalties -- two for pass interference.
Carolina rookie Tauren Poole scored on a 1-yard touchdown run to tie it at 13 just before halftime.
Carolina's defense settled down after a shaky start.
Rookie weak side linebacker Luke Kuechly, the No. 9 overall pick in the NFL draft, made an immediate impact in his first NFL action by stripping Foster in the first quarter after an 11-yard gain.
The Panthers played without their defensive leader Jon Beason, who sat out after tweaking his hamstring in practice. Phillips, his replacement at middle linebacker, had Carolina's other turnover, although he seemed as surprised as anyone when Schaub threw it right at him.
The Texans won the NFC South championship last year after rallying behind backup quarterback T.J. Yates, who took over after Schaub went down in a 37-9 win over Tampa Bay on Nov. 13. Yates played the better part of two quarters Saturday night, finishing 8 of 12 for 89 yards passing. He led two drives which resulted in field goals, but unlike last year couldn't get the Texans into the end zone.
John Beck, was 4 of 6 for 46 yards and led one touchdown drive.
Undrafted rookie Case Keenum, the NCAA's career leader in yards passing, touchdowns, and completions at the University of Houston, completed 2 of 3 passes for 33 yards for the Texans.
Houston's defense, which finished second in the league last year, registered seven sacks -- four of those on Jimmy Clausen.
Houston's only offensive touchdown came on 3-yard touchdown run by rookie Jonathan Grimes.
For the most part, Carolina fans didn't have much to cheer about.
But rookie Joe Adams, the team's fourth-round draft pick, gave the crowd a thrill when he changed field, avoided several tacklers and returned a punt 39 yards in the fourth quarter. The Panthers have ranked near the bottom of the league in punt return average the last several years and hope Adams can give them a spark in the return game.