Luke Moore headed home in the 83rd minute to give the Swans an enormous victory over the pre-round league leaders who fell behind in their quest for the title as Manchester United hit the top with a victory over West Bromwich Albion.
Overall it was a lackluster affair which provided a lot less scoring chances than would have been thought prior as City stuttered to lose slight touch of their 44-year dream for a first division title.
Swansea's Joe Allen was the culprit for a big miss in the 51st minute when Danny Graham's low cross from the right went begging but the City defence could have been praised for their great pressure to deny the Welshman.
City boss Roberto Mancini thought his side had delivered a vital equaliser but the linesman had adjudged Richards to be offside as the Eastlands club were denied a point to slip back to second on the table in what could be a late-season stutter.
TRIBAL ASKS: Wow! Is this City's time to start crumbling under the pressure of the title hanging over their head?
Liberty Stadium, Swansea - 20,510