Two first-half goals from Ryan Watson and Callum Morton set them on their way to victory in the League Two play-off final and a return to the third tier for the first time since 2018, while Sam Hoskins and substitute Andy Williams capped things off late on.
It was also third time lucky for boss Keith Curle, who had previously lost as a manager in the League Two play-offs with Mansfield and Carlisle.
For Exeter, who finished with 10 men after Dean Moxey’s red card just before the hour, it was a third loss at this stage in four years, having also been beaten at Wembley in 2017 and 2018. They will now prepare for a ninth consecutive season in League Two.
Northampton had to make a dramatic comeback to reach the final, but they got off to a far better start at Wembley than they did in the semi-final as Watson fired them in front on 11 minutes. The midfielder had missed a penalty in the first leg of their semi-final at Cheltenham, so would have been particularly delighted to see his deflected effort from the edge of the box sneak beyond Jon Maxted in the Exeter goal.
Matt Taylor made changes after the break but it went from bad to worse for his side on 59 minutes as Moxey saw red for a daft, wild lunging challenge on Watson.
Northampton then romped home with 10 minutes to go they put the icing on the cake as Mark Marshall raced into the box and squared for Hoskins to turn home, and in the 89th minute they put the cherry on top of that as Williams poked in from close range after Exeter failed to deal with a long throw into the box.
Northampton will begin the 2020/21 campaign in League One, while Exeter will remain in League Two.