Clinical finishing from Chelsea hitman Adrian Mutu condemned struggling Everton to another defeat and yet another game without scoring.
Everton without a goal in the last three Premiership matches could and should have been ahead in the first minute. A weak ball from Thomas Gravesen to Tomasz Radzinski saw Jon Terry slip to gift the Canadian a clear run at goal, but with just Carlo Cudicini to beat, the striker put his shot wide of the right-hand post.
A minute later Kevin Kilbane also had a good opportunity in front of goal, left unmarked from a corner, but he headed over.
Alex Nyarko was making his first Premiership start in two years after an altercation with a fan forced him to quit the club and the midfielder almost made amends for his absence on 22 minutes.
Nyarko hit a 22-yard screamer which flew past the static Cudicini but it hammered back off the underside of the bar.
Terry made a second error minutes later, again giving Everton the ball with the goal gaping, he put his clearance straight to the feet of Wayne Rooney with Cudicini on the edge of the penalty area, but Rooney's lob landed a foot wide.
Chelsea's best chance of the first half fell to Joe Cole on 34 minutes, but his low left-foot shot drifted agonisingly wide but the Londoners eventually took the lead in the second half on 48 minutes.
Geremi whipped in a cross from the right which evaded the Everton back four and Jimmy Floyd Hasselbaink, leaving Adrian Mutu to head home at the far post.
Chelsea should have got a second on 57 minutes, Hasselbaink put Geremi clear in the box and he played the ball to Frank Lampard, but his shot was brilliantly smothered by keeper Nigel Martyn.
Everton brought on James McFadden and Francis Jeffers on 64 minutes to breath new life into their flagging side and Scottish winger McFadden made an immediate impact, playing in Rooney on 71 minutes, but he failed to convert.
Then a glaring miss from fellow sub Jeffers on 83 minutes condemned the Merseysiders to defeat.
Gary Naysmith had chipped a ball to the far post with Jeffers unmarked one yard out, but his poor header glanced off his head and went the wrong side of the post leaving Goodison Park groaning.
Cudicini saved well from Thomas Gravesen deep into injury time as Chelsea secured maximum points and Everton were left rueing missed chances.