Schaub completed 17-of-30 passes with an interception as the Texans (3-0) began a season with three straight wins for the first time in franchise history.
Arian Foster carried the ball 25 times for 105 yards and also hauled down a 3-yard touchdown catch for Houston.
Peyton Manning led the Broncos (1-2) on a late comeback try, hurling a pair of fourth-quarter scores, but it wasn't enough and Denver lost its second straight.
Manning finished 27-of-52 for 325 yards and Eric Decker made seven grabs for 123 yards.
Ray Rice could return to the NFL within a month
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