Villa dominated possession for most of the first half but failed to turn pressure into goals, with Christian Benteke heading wide while in plenty of space inside the Sunderland area.
The visitors were almost punished for their lack of creativity in front of goal but Lee Cattermole fired over from the edge of the box on the stroke of half-time.
Paul Lambert's side were once again on top at the beginning of the second period and made the breakthrough in the 55th minute when the dangerous Benteke climbed highest inside the box to head the ball into the path of Gabriel Agbonlahor, who then stabbed the ball past Simon Mignolet from close range.
Sunderland had claims for a penalty denied just moments after Agbonlahor's goal but the referee refused to point to the spot despite John O'Shea's header appearing to strike Benteke's raised arm.
Villa had an opportunity to double their lead on the counter attack but Andreas Weimann made poor contact with an effort that Mignolet was able to easily collect.
However, the visiting defence held firm to claim a vital three points and move further away from the relegation zone.