The 28-year-old netted his second goal in five days to secure the hosts' second win of the season and close the gap to safety to just three points.
Bardsley met a long ball from Wes Brown in the 21st minute of the game, shrugged off the attentions of Martin Demichelis and James Milner before firing past Costel Pantilimon.
It is Sunderland's fourth consecutive 1-0 win over City at the Stadium of Light, and Bardsley admitted it was a big win for the club.
"Midweek was a big win but to get those three points was massive," he said.
"Manchester City are a top team and we knew it would be tough. Most of all when we had the ball we had great quality.
"We were unbelievable defensively. We knew they would press second half. We were resilient and showed great desire to win that football match."
Bardsley spent the early part of the season excluded from the first-team squad under ex-manager Paolo Di Canio, but he has been recalled by new boss Gus Poyet and is enjoying a resurgence in form.
He thanked the Uruguayan for showing faith in him and giving him a second chance at the club.
"The players were nervous earlier in the season (under Di Canio)," he added. "But the manager (Poyet) has shown great belief and got the players playing the way he wants.
"I owe him a lot because he has brought me in from the cold and I want to repay him."
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