Jack Clarke opened the scoring just before the hour mark when he cut in from the right and fired a shot into the top corner.
Tony Mowbray’s side appeared to be heading towards a third consecutive victory before Trai Hume brought down substitute Jay Dasilva in the box, allowing Nahki Wells to convert from the penalty spot.
Here’s how Phil Smith rated the Sunderland players at the Stadium of Light:
5. Leo Hjelde - 6
One or two loose passes but steady enough on his return to the side at left back. Bristol City very rarely threatened down his flank. 6 Photo: Frank Reid
6. Dan Neil - 6
Had a good first half and moved the ball well, looked to tire a little late on in the second. 6 Photo: Frank Reid
7. Pierre Ekwah - 7
A huge improvement from his performance earlier in the week. Dominated the midfield duels during the first half in particular and got about the pitch very well. Encouraging. 7 Photo: Frank Reid
8. Chris Rigg - 6
Good energy and got into promising attacking positions on a couple of occasions. Moves the ball nicely when he drifts infield but no significant impact in the final third on this occasion. 6 Photo: Frank Reid