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Osweiler, benched on Dec. 18, got his job back this week with Tom Savage out with a concussion, and played his best game of the season to give the Texans their first playoff victory since the 2012 season.
Houston bounced back after an embarrassing 30-0 wild-card loss to Kansas City last season to advance to face either the Chiefs or New England in the divisional round next weekend.
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The Raiders' first trip to the playoffs since the 2002 season, when they went to the Super Bowl, ended with a thud behind the struggles of third-string rookie Connor Cook. He threw for 161 yards with one touchdown and three interceptions against the NFL's top-ranked defense.
He became the first quarterback in NFL history to make his first start in a playoff game after MVP contender Derek Carr broke his leg two weeks ago, and Matt McGloin injured his shoulder on Sunday. His performance wasn't helped by star left tackle Donald Penn missing the game with a knee injury, which ended a streak of 160 straight starts.
Houston (10-7) led by 13 at halftime and made it 27-7 on a 1-yard run by Osweiler early in the fourth quarter.
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Brock Osweiler, Houston's much-criticized quarterback, threw for one TD and ran for another.
Since the Texans did defeat the Raiders, they will advance to the divisional round. Who they play will depend on the Miami/Pittsburgh game that will be held Sunday at noon. If the Steelers win, the Texans will play at New England Patriots next Saturday. If the Dolphins win, the Texans will play at Kansas City Chiefs next Sunday.
The Associated Press' Kristie Reiken contributed to this report.