Hosts Durham had scored 392 in their first innings in the match at Chester-le-Street.
The 28-year-old Rushworth finished with match figures of 15-95, the best by a Durham bowler in a county championship fixture.
Relegated Northants lost by an innings and 219 runs, their 12th defeat in 15 matches this season.
(Reporting by Tim Collings; editing by Ken Ferris)
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