The home side went into the game with ambitions of pipping Burton to lift the title but Plymouth shocked Micky Mellon’s men with first-half goals from Bobby Reid and Kelvin Mellor.
With Burton winning, Shrews would not have lifted the title regardless but their inability to mount a comeback meant they suffered a second home league defeat of the campaign.
There were just three minutes on the clock when Mellor burst forward down the right and his low cross was confidently steered home by the impressive Reid.
James Colins tried to engineer an instant response but his shot was well saved by Luke McCormick.
At the other end Zak Ansah and Reid both went close to doubling the advantage before Mellor did just that a minute before the interval, finishing coolly from close range after the ball kindly ran his way.
Shrewsbury surged forward in search of a way back in the second half.
A deflected effort from Ryan Woods produced a fingertip save from McCormick and Tyrone Barnett fired narrowly off target from just outside the box.
Plymouth, who will face Wycombe in the semi-finals of the play-offs, almost added a late third but substitute Tyler Harvey’s 25-yard free-kick was brilliantly tipped over the bar by Jayson Leutwiler.