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.
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.
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 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.
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.
