Brian Hoyer, who replaced Ryan Mallett for Houston (1-4) in the second quarter, threw a pass up for grabs that was intercepted by Mike Adams with less than 2 minutes left.
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Greg Ward Jr., who completed 16 of 18 passes for 243 yards, led the Cougars with 82 yards on 14 carries, finding the end zone once in each quarter.
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One of the six remaining undefeated NFL teams will be on the field in Cincinnati on Sunday when Seattle visits.