Bottom club Sheffield United survived for more than 30 minutes with 10 men to claim only the fourth Premier League win of their disappointing season and dent Aston Villa's European ambitions.
David McGoldrick gave his side a first-half lead from inside the six-yard area after being picked out by George Baldock following a lovely move that started inside the Blades' half.
United defender Phil Jagielka was sent off after half-time for a foul on Anwar El Ghazi after referee Robert Jones viewed the incident on a pitchside monitor and changed the yellow card he had initially given him to a red.