The Black Cats took a first-half lead after fine strikes from Elliot Embleton and Nathan Broadhead inside the opening 14 minutes.
Yet a disjointed start to the second half saw Shrewsbury draw level after goals from Josh Vela and former Cats defender Tom Flanagan.
Nathan Broadhead then scored a stoppage-time winner when he headed home Jack Clarke's cross.
Our chief SAFC writer Phil Smith has delivered his verdict on how each Black Cats player fared at the Stadium of Light:
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1. Anthony Patterson - 6
Little he could do about either goal and it was almost another stunning save to deny Flanagan’s equaliser at close range. 6 Photo: JPI Media
2. Carl Winchester - 5
Guilty of being a touch sloppy in possession at times even if for the main he defended well. 5 Photo: JPI Media
3. Bailey Wright - 6
Steady defensively and won the bulk of his duels against Bowman. 6 Photo: JPI Media
4. Dennis Cirkin - 6
Started the game really well and played his part in the second goal. Stepped out in possession well for most of the game. 6 Photo: JPI Media