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:
1. Anthony Patterson - 6
Very little to do with Bristol City very poor in possession, but did his job with little fuss. 6 Photo: Frank Reid
2. Trai Hume - 6
Got away with one or two lapses in defence but also made a couple of good challenges and put in some good crosses as well. 6 Photo: Frank Reid
3. Dan Ballard - 7
Had a good game, dominant in his defensive duels and playing the ball out well to those in front of him. Bristol City rarely threatened in an admittedly fairly poor contest. 7 Photo: Frank Reid
4. Luke O’Nien - 7
Made one excellent block to keep his side level just before half time, dropping into to clear a goalbound effort from Twine off the line. Rarely troubled otherwise. 7 Photo: Frank Reid