Minutes before he scored, Ivanovic had been booked by Referee Kevin Friend for catching Christian Benteke with an elbow, a lenient decision by the referee and one that infuriated Villa boss Paul Lambert.
That was not the only controversial decision in the game. Late on, John terry blocked got away wit a hand ball in the penalty area, a decision that on another night could have resulted in a penalty to the visitors.
Just like they did against Hull on Sunday, Chelsea scored early again tonight when Antonio Luna deflected the ball into his own net following a Brad Guzan save from an Eden Hazard shot.
But Chelsea struggled to break down Villa and it was not a surprise when Benteke scored his third goal of the season with the final kick of the first half.
As someone said on Twitter after the game, last season Chelsea drew this game or maybe even lost it. But Jose Mourinho is giving the team confidence that they did not have under Benitez and because of that they were able to grind out a won tonight.
Mourinho has never lost in 62 top-flight matches at Stamford Bridge and next Monday takes his side to Manchester United for an early title bout, where transfer target Wayne Rooney is sure to be the focus of attention.