Everton 0 Chelsea 1
By Paul Higham
Last Updated: 01/01/70 1:00am
Claudio Ranieri's men were on the back foot for most of the match and had Carlo Cudicini, along with Francis Jeffers missing a sitter, to thank for their three points.
Mutu had a shot straight from the kick off at Goodison Park, but it was the hosts that should have taken the lead within a minute when Tomasz Radzinski was sent clear by Thomas Gravesen but slotted his finish just wide of the post.
Kevin Kilbane then headed just wide from a corner as David Moyes' men looked to upset the odds in a half when they more than held their own against the visiting millionaires.
Wayne Rooney then had an effort from the same spot as he marked his arrival in The Premiership against Arsenal but put too much curl on his shot and the ball fizzed into the hands of Cudicini.
Everton's forgotten man Alex Nyarko was looking to get back into the good books of the Toffees faithful, and he nearly did the trick moments later as he fired in a vicious swerving effort that smacked against the bar from 20 yards with Cudicini beaten.
Radzinski had another golden opportunity a minute into the second half as he found himself free 12 yards out but his shot on the turn was well turned over by Cudicini.
Although Chelsea had barely threatened all afternoon, they took the lead three minutes after they should have been behind, when Mutu arrived at the far post to nod in Geremi's cross with a diving header.
Geremi scuffed his shot just after the hour as Chelsea played mainly on the break but his bobbled effort still could have gone in after a fumble by Nigel Martyn, while Jimmy-Floyd Hasselbaink flashed a fierce shot just over from 25 yards out.
James McFadden and Jeffers were thrown on by Moyes as Everton piled forward for an equaliser, and Jeffers had a glorious chance to grab a deserved leveller when Gary Naysmith floated over a superb cross for him, only for the on-loan Arsenal striker to somehow head wide from just five yards out.
Gravesen then broke through manfully in the dying seconds and fired in his effort from the edge of the box but Cudicini was there again to push the ball away to earn Chelsea the three points.