Jores Okore ended the Villans' goal drought just shy of 11 hours with an equaliser to Eden Hazard's opener but the Serbian defender saw them off with a powerful effort
The Blues took the lead almost immediately through Eden Hazard but the Villans struck back through Jores Okore straight after half-time, ending their goal drought just short of 11 hours of play.
But Chelsea's quality told and Branislav Ivanovic secured the points with a powerful finish in the 66th minute.
Before Okore's goal, Villa had gone 659 minutes without finding the net - the fourth-longest barren spell in Premier League history - but for Paul Lambert and his side, the end of their scoreless run will be of little consolation, with the Villans now winless in nine league matches and just two points above the relegation zone.
|VIEW FROM VILLA PARK
|By Sam Lee
Jose Mourinho had never won at Villa Park in five previous attempts but his Chelsea side got the job done here to move seven points clear of Manchester City.
Even a rare Aston Villa goal, their first in just shy of 11 hours, did not spook the Blues and Mourinho will surely be pleased, even if his mood of late has been dark and dour.
Not too many of his players stood out but an important victory is in the books and, with City only scraping a draw at home against struggling Hull City, he will be heading back to London in high spirits.
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 over Fabian Delph's cross in the 19th minute.
Brad Guzan had to parry away Oscar's fierce shot at the near post three minutes later as Chelsea went in search of a second, though a stiffened Villa back line kept the leaders at arm's length until the interval.
The hosts 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 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.