The visitors took an early lead from the penalty spot which saw Ricardo Rocha receive a red card for bringing down Darren Bent. The latter then put the Black Cats ahead.
Sunderland enjoyed numerical advantage until early in the second half when Lee Cattermole was dismissed for two bookable offences.
Patrick Vieira started for City, but it was another newcomer who caught the eye, Adam Johnson.
Emmanuel Adebayor then added a second in the 73rd minute to pile the pressure on relegation-threatened Bolton.
Wigan and Stoke fought out an entertaining 1-1 draw at the DW Stadium as both side's inch clear of the relegation places.
The Latics scored on 14 minutes through Paul Scharner but Stoke fought back and were rewarded in the 74th minute when Tuncay Sanli headed home Matthew Etherington's right-wing cross.
The Cottagers were two up by the interval courtesy of Danny Murphy and David Elm.
Bobby Zamora ensured a comfortable second 45 minutes when he curled a low free-kick into the bottom corner just after the break.