Victory was Jose Mourinho's first at Villa Park in five attempts, and Chelsea's day was made even more enjoyable with Manchester City's surprise 1-1 draw at home with Hull City.
Eden Hazard had given Chelsea an early lead inside 10 minutes, before Jores Okore ended Villa's long goal drought with a header at the start of the second half.
Before the defender's effort, Villa had gone 659 minutes without finding the net - the fourth longest barren spell in Premier League history.
Villa responded well to going behind and Gabriel Agbonlahor - recalled for Christian Benteke as one of three changes - headed Fabian Delph's cross over in the 19th minute.
Brad Guzan had to parry Oscar's fierce shot away at the near post three minutes later as Chelsea went in search of a second, though a stiffened Villa backline kept the table toppers at arm's length until the interval.
Chelsea failed to sufficiently clear Carles Gil's corner and as the ball came back to the Spaniard, his cross was headed home at the far post by Okore.
Cesar Azpilicueta's initial cross was blocked by Okore, before the Chelsea man dug out a bouncing ball towards Ivanovic, who sent an excellent left-footed volley into the top left-hand corner from 16 yards.
