Washington's Graham Gano missed a 52-yard field goal in the first possession of overtime, and the Texans (2-0) started with the ball at their own 42.
Two downs later, Rackers split the uprights for the victory, giving the Texans a franchise-best six straight wins dating back to last season.
Schaub ended up going 38-for-52 with 497 yards, three touchdowns and an interception.
Donovan McNabb piled up 426 yards passing for the Redskins (1-1), going 28-of-38 with one touchdown and no pick-offs.
Santana Moss hauled down 10 passes for 89 yards for Washington.
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