On three previous occasions the hosts had won this fixture by one goal, and that proved to be the case again thanks to Bardsley's 21st-minute strike.
Latching onto Wes Brown's clever through ball, the full-back shrugged off James Milner inside of the area before calmly slotting past the onrushing Costel Pantilimon, much to the delight of the home crowd.
City came close to equalising via Sergio Aguero when he headed wide from Aleksandr Kolarov's first-time cross, but Manuel Pellegrini's side endured a majorly frustrating first-half with clear-cut chances limited.
Jesus Navas was introduced for the second-half and the winger almost made an immediate impact when his goal-bound effort was blocked on the line by Ki Sun-Yeung.
Aguero and substitute Edin Dzeko both tested Vito Mannone as the visitors piled on the pressure, but Sunderland held on to secure Gus Poyet's third win since taking charge.
For Pellegrini's men, it was a fourth defeat in six league outings away from the Etihad Stadium this summer, and a return of just four points from a possible 18 on the road is severely hampering their title chances.
They arrived at the Stadium of Light having scored 14 goals in their past three games in all competitions, but as Sunderland defended as if their lives depended on it, they were unable to find a way past Vito Mannone.
It was just a second league victory of the season for the home side, and it served to boost their survival hopes and once again justify manager Poyet's approach in front of a crowd of 40,137.
The visitors started positively and Bardsley had to make an important header to deny Alvaro Negredo a seventh-minute header at goal from Kolarov's cross, and Mannone plucked James Milner's long-range drive out of the air seconds later.
However, the home side might have gone ahead when Sebastian Larsson picked out lone striker Fletcher with an inviting right-wing cross, but the Scotland international mistimed his header and sent it well wide.
Larsson was perhaps fortunate to escape further punishment for a late challenge on Javi Garcia, and the City man's mood was not improved when Mr Dean cautioned him for a later challenge on Fletcher. But by that point, the Black Cats were ahead.
Wes Brown, starting his first Premier League game since January 21, floated the ball over the top for Bardsley to shake off Milner before cutting inside and curling a shot across Pantilimon, once again preferred to England international Joe Hart.
City's response was tepid and Sunderland created a series of half-chances to increase their lead, although Ki Sung-yueng overhit a through-ball to the unmarked Fletcher and defender Martin Demichelis got to Emanuele Giaccherini's 36th-minute cross marginally ahead of the Scot.
But Mannone did not have any further saves of note to make as Poyet's 4-1-4-1 formation and instructions to keep possession paid off handsomely.
Navas might have equalised within five minutes of his arrival but Bardsley made a vital block.
The Spain international steered a 54th-minute cross along Mannone's goal, but it was Ki who came closest at the other end four minutes later when he blasted a right-foot shot just wide.
The goalkeeper then had to palm away Aguero's dipping effort three minutes later and as time ran down, Pellegrini replaced Negredo with Dzeko and Richards with Pablo Zabaleta.
Dzeko almost did the trick within seconds when he forced a flying save from Mannone with Aguero unable to make the most of the rebound.
Poyet's men were forced to weather a relentless assault as the final whistle approach, but with Brown marshalling his forces outstandingly at the back there was simply no way through for City.