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As expected, Chelsea dominated the opening stages and it took them just seven minutes to open the scoring.
Willian was set free by Branislav Ivanovic down the right flank but saw his initial shot parried by Brad Guzan. The ball fell again at the feet of the Brazilian, who had the presence of mind to square the ball to Oscar, who was left with the simple task of tapping home from a few yards out.
Willian looked lively and sent another shot into the side netting in the 15th minute, but Villa reminded the Stamford Bridge crowd of their threat when Aly Cissokho picked up a loose ball from a corner and hooked an effort narrowly wide of the post.
Cesc Fabregas should have tested Guzan at the other end after half an hour, but the Spaniard dragged his shot wide of the post before Diego Costa had his first sniff of goal with a header which was too close to the American stopper.
Villa had two chances of their own either side of the half-time whistle when Fabian Delph shot wide from the edge of the box before going close once more with a long-range effort in the 47th minute.
Nathan Baker then saw his shot nestle on the roof of the net as Villa continued to cause problems for the Chelsea back line.
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However, Costa continued his incredible run of form by netting his eighth league goal of the season when he nodded home from Cesar Azpilicueta's cross to make it 2-0 after an hour.
Oscar almost got his second of the afternoon a few minutes later, but after rounding Guzan, Cissokho made a last-ditch goalline clearance to deny him.
Costa then came close to connecting with Eden Hazard's low centre after mesmerising wing play from the Belgian as Chelsea asserted their dominance following their second goal.
Willian grabbed his second goal of the afternoon and Chelsea's third in the 79th minute with a tap-in after Guzan could only parry another Costa shot as the home side continued their formidable start to the season.