Premier League: Chelsea 3 Aston Villa 0
Costa has been nursing a hamstring problem, but there were no signs of an injury as he continued his outstanding start to his Chelsea career by finding the back of the net with a towering second-half header on Saturday.
Oscar opened the scoring early in the first half with his second goal in as many games and that set the tone, as Jose Mourinho's league leaders maintained their ominous early-season form with a deserved win.
Costa doubled their lead just before the hour-mark and Willian added the third with a tap-in, his first goal of the season, to round off another impressive display from free-scoring Chelsea, who have now scored 19 goals in their first six top-flight games.
The London club suffered a costly 1-0 defeat at Aston Villa when the two sides last met back in March, which dealt a major blow to Chelsea's title hopes, but they gained revenge as Paul Lambert's men failed to recover from Oscar's early strike.
Villa have now suffered back-to-back defeats after losing their unbeaten record against Arsenal last weekend.
Ramires was ruled out due to a muscular injury, so Oscar was given the nod to replace him in the only change to the side that drew 1-1 at Manchester City last Sunday.
Nathan Baker and Ashley Westwood returned to the Villa side after recovering from a virus which kept them out of last Saturday's defeat against Arsenal, so Ciaran Clark and Carlos Sanchez dropped to the bench.
Chelsea were indebted to John Terry after only six minutes, when the he got on the end of Aly Cissokho's inviting cross with a great defensive header as Kieran Richardson charged into the six-yard box behind him.
Villa were caught out just a minute later, though, when two of the home side's Brazil internationals combined to put them in front.
Willian raced away down the inside right and, after his shot was palmed straight back to him by Brad Guzan, the former Anzhi man cut the ball back to the onrushing Oscar to side-foot home despite the best efforts of Alan Hutton.
The visitors responded and Cissokho fired just wide with his right foot after Chelsea failed to deal with a corner from the right.
Chelsea were dominant and Willian laid on another chance when he picked out Costa with a cross, but the Brazil-born striker's powerful header was saved by Guzan.
The visitors showed little ambition going forward in the first half, but Fabian Delph gave Chelsea a warning just after half-time when he evaded a couple of challenges before unleashing a venomous left-footed strike from long range that flashed past the far post.
Baker rose highest to meet a free-kick, but headed onto the roof of the net and Costa ought to have made him pay when he failed to get a good contact on his header after Branislav Ivanovic picked him out.
The former Atletico Madrid man was not to be denied 59 minutes in, though, when he got in front of his marker to head home a Cesar Azpilicueta cross from eight yards out to round off a slick Chelsea move.
Oscar must have thought he had his second when he poked the ball beyond Guzan, but Cissokho raced back to clear just before it could cross the line.
Willian then got his name on the scoresheet, converting from point-blank range after Costa's shot was saved by Guzan 11 minutes from time.