Pedant alert - they didn't actually beat us that day:
Manchester City v Aston Villa 1980/81
Withe did have a stormer and Villa outplayed us all afternoon, but two late goals (a Dennis Tueart penalty and what I think was Ray Ranson's only goal for the club) rescued us. We'd lost 4-0 at home to Sunderland the previous midweek and the crowd had started to turn against the team somewhat until we were awarded that (rather soft) penalty.
FWIW, they last beat us in the league at our place at the end of Stuart Pearce's final season, winning 2-0 as we continued our run of no goals at home since New Year's Day. They did also manage a League Cup win, 4-2 after extra time in Mancini's period at the helm when we fielded a much-changed side.