Bobby Reid and Kelvin Mellor scored first half goals at the New Meadow to end Shrewsbury’s hopes of claiming the title.
The victory meant Argyle secured seventh spot and will now face Wycombe Wanderers in the two-legged play-off semi-finals. The first match will be at Home Park on Saturday, May 9.
Argyle manager John Sheridan is relishing the play-offs and believes teams will be wary of his side, especially after the performance they produced at Shrewsbury.
“On our day, we’re as good as any team in the league,” said Sheridan.
“We have got as good a chance as anyone and that is the way we are going to prepare – believing that we can get up.
“We will prepare properly in our week for what’s going to be a good atmosphere, a full house. We’re at home first, so we would like to go into the game and try to get an advantage, but the main thing is you keep yourself in it for the second leg.”