Northampton's relegation to League Two was confirmed after they suffered defeat against play-offs-bound Leeds while Carlisle beat Millwall 2-0.
Luciano Becchio nodded Leeds in front from Ben Parker's cross before Luke Guttridge and Leon Constantine went close for the Cobblers.
But Jermaine Beckford netted his 34th goal of the season in the bottom left-hand corner on the hour.
And substitute Robert Snodgrass added the third with an injury-time volley.
Leeds will visit Millwall in the play-off semi-final first leg on Saturday 9 May, with the home leg on Thursday 14 May.
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Leeds:
Ankergren, Douglas, Naylor, Marques, Parker (Richardson 67), Robinson, Howson, Kilkenny (Snodgrass 57), Delph, Beckford (Grella 77), Becchio. Subs Not Used: Lucas, Johnson.
Goals: Becchio 44, Beckford 59, Snodgrass 90.
Northampton:
Dunn, Dolman, Crowe, Hughes, Jackman, Anya (Larkin 63), Osman, Guttridge, Holt (Davis 63), Constantine, Akinfenwa. Subs Not Used: Walker, Watts, Coke.
Booked: Dolman.
Att: 34,214
Ref: Andy Penn (W Midlands).
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