Goals from Ryan Watson and Callum Morton gave Northampton the ideal start while their task was made easier when Exeter's Dean Moxley was sent off early in the second half.
Sam Hoskins and Andy Williams added further strikes to rubber-stamp Northampton's return to League One after a two-year absence.
Northampton were seventh in the standings, occupying the last play-off position, when the season was halted by the COVID-19 pandemic in March.
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Clubs voted to end the campaign early, deciding the final table on points per game.
Northampton lost the first leg of their semi-final clash with Cheltenham Town 2-0 but staged a remarkable comeback in the second leg, which was also played behind-closed-doors, to win 3-0 and advance to the final. (Reporting by Richard Martin Editing by Christian Radnedge)
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