Tony Mowbray’s side were denied a penalty in the first half when Patrick Roberts was brought down and instead booked for diving.
The visitors dominated the second half but couldn’t make a breakthrough, before Matthew Pennington opened the scoring for the hosts from a corner.
Sunderland then scored two stoppage-time goals as Ross Stewart and Luke O’Nien turned the match around.
Here’s how Phil Smith rated the Sunderland players:
9. Patrick Roberts - 7
Should have had a penalty in the first half and was somehow booked for diving when clearly tripped. Kept going and deserved to be on the winning side. 7 Photo: Martin Swinney
10. Jewison Bennette - 6
Showed his turn of pace on a couple of occasions to get past his marker and create an opening. Got stuck in and will be better for the experience against a physical opponent. 6 Photo: Frank Reid
11. Amad - 7
Took him a while to get into the game but got the late assist for O’Nien and went close on more than one occasion. Shrewsbury couldn’t get the ball off him after the opening exchanges. 7 Photo: Frank Reid
12. Ross Stewart (sub) - 7
Fairly quiet after being introduced but once again found a way to get on the scoresheet. What a run he is on. 7 Photo: Frank Reid