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.
But for Paul Lambert and Villa, the end of their scoreless run will be of little consolation to a side that is now winless in nine league matches and just two points above the relegation zone.
Chelsea, meanwhile, will be buoyed by putting further daylight between themselves and City, as they go in search of a third league title under Mourinho.
The visitors made an assured start and were ahead inside eight minutes when Oscar fed Willian, whose pass was swept home first time by Hazard from 10 yards.
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.
Villa began the second half brightly and were level within three minutes of the restart.
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.
Willian twice fired narrowly wide as Chelsea attempted to retake the lead, and they did not have to wait too long as Ivanovic produced a superb strike.
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.
With their lead re-established, Chelsea were content to cruise for the remainder of the match, and Mourinho was able to give a debut to Juan Cuadrado, who replaced Willian with 10 minutes remaining.
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