Goals from Murray Wallace and Sam Manton were enough to condemn Swindon to the drop despite a brilliant strike from Rohan Ince.
The struggling Robins had to win to stand any chance of staging a great escape but found themselves behind after only six minutes.
Goalkeeper Lawrence Vigouroux fumbled a cross and Wallace was on hand to slot home.
Substitute Manton heaped more misery on Luke Williams' side moments after coming on.
Manton was given too much room in the box to tuck the ball past a helpless Vigouroux.
Brighton loanee Ince gave the home fans hope when he smashed an unstoppable long-range shot into the top corner with five minutes left.
But that goal was too little to late to rescue the Robins' League One status.