Blues boss Joe Mourinho insists Costa, a £32 million ($51.9 million) pre-season signing from Atletico Madrid, is still not fully fit and is only capable of playing one game a week.
But he looked in fine fettle at Stamford Bridge as he struck in the second half to take his season’s tally to eight goals before creating Willian’s late strike.
Oscar’s early opener had threatened to open the floodgates and Mourinho’s men never looked troubled as they saw out this one-sided contest with ease.
Villa knew their good start to their season would be tested by the leaders and, having lost convincingly against Arsenal last time out, they were never at the races in west London.
Paul Lambert opted to pack his Villa midfield and then look to break with pace at every opportunity.
That method almost worked to perfection in the second minute when Chelsea goalkeeper Thibaut Courtois was forced to make a dash off his line to smother Fabian Delph following a quick breakaway.
But Lambert’s plans went out the window when Brazil playmaker Oscar opened the scoring in the seventh minute.
Willian’s shot was blocked by Villa goalkeeper Brad Guzan, but the rebound saw fell kindly for the Brazilian winger to tee up his compatriot for a close-range finish.
The travelling Villa supporters, who are still haunted by their 8-0 defeat at Bridge just over two years ago, must have feared the worst and rampant Chelsea almost extended their lead in the 15th minute.
Costa’s clever flick freed Willian and his cross was deflected inches wide off Alan Hutton with Guzan stranded.
Villa’s best hope of unsettling Chelsea lied in a set-piece play and that almost contributed to a 19th minute leveller.
Ashley Westwood’s corner caused a scramble in the Chelsea penalty area, but Aly Cissokho could only steer his shot wide under pressure.
That was a rare moment of panic as Villa did their best to keep Chelsea at bay.
-Wake up call –
To Villa’s credit, Mourinho’s men were largely restricted to long-range efforts as they looked to increase their lead.
Once they finally came within range, Spain midfielder Cesc Fabregas drove wide from the edge of the box on the half-hour mark.
The impressive Willian then crossed for Costa to force Guzan into a routine save from a tame header.
Villa were happy to sit and soak up pressure as everything was played in front of them.
Content to frustrate the hosts, Villa finally broke out and threatened just two minutes after the restart.
Delph’s quick feet earned him some extra room and the England midfielder saw his 25-yard shot curl just the wrong side of the post.
There were more anxious faces in the stands when Villa defender Nathan Baker headed onto the top of Courtois’s net.
But it was the wake-up call Chelsea needed and Costa continued his hot-streak in the 59th minute, edging ahead of Baker to score with a powerful header from Cesar Azpilicueta’s cross.
Oscar’s free-kick saw John Terry head narrowly wide but it was only a brief respite for Villa as Willian got the goal his display deserved.
Costa tormented the Villa defence again and after his shot was beaten out by Guzan the ball rebounded into the path of Willian who swept the ball into an empty net in the 79th minute.