Villa levelled the scores just past the hour after the hosts had taken a 30th-minute lead, but a late double from Jermain Defoe ensured that the Black Cats picked up all the points.
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Sunderland made the breakthrough in the 30th minute when Patrick van Aanholt's deflected effort found its way past Brad Guzan and the hosts led at the end of a first period that lacked clear opportunities.
Adam Johnson set up Defoe for 2-1 Sunderland in the 72nd minute, however, before the former England international bagged his second of the match in stoppage time after finding space outside the box. Defoe thought that he had scored a hat-trick two minutes later, but the strike was ruled out for offside.
Villa, who have still only won one league game this season, actually had more of the possession at the Stadium of Light, but they struggled to create clear chances throughout the match and are now seven points off 19th-placed Sunderland at the bottom of the table.