The Blues remain unbeaten away in the league in 2008 but there is huge disappointment as a win is allowed to slip from grasp late on.
Chelsea were as good in the second half as we were poor in the first and two Frank Lampard goals looked to have won it following Clint Dempsey's early opener for Fulham.
But the same scorer for the home side found the net in the 89th minute to leave Chelsea three points off the pace on a day Liverpool won well.
There were two changes from the Boxing Day win with Scolari freshening it up with a spot of rotation - Deco in for Ballack and Malouda for Anelka, the Frenchman asked to play on the left of a front three that also contained Didier Drogba and Joe Cole.
When the game began on a cold and sunny afternoon besides the Thames, the first shot on-target was Lampard's fifth-minute 25-yard dig, straight at Schwarzer after the Fulham keeper had invited pressure when kicking out poorly.
On eight minutes Drogba could only find the side-netting from a tight angle after Malouda had slipped him through down the inside left channel.
But it had been a decent enough start by the visitors, not maintained as a minute later, Fulham took the lead.
It was a free kick that did the damage, even without the presence of the injured Jimmy Bullard for the home side. The ball from the left by Davies was played dangerously into the area of uncertainty at the far post and as Mikel got caught out by a deflection, Dempsey took charge and turned the ball in from point blank range.
There were just 10 minutes gone. Chelsea's initial response was not promising but on 18 minutes, Drogba, whose presence was leading to the Fulham defence standing off a yard or two, should have scored. Turning cleverly into space, his shot from the right was dragged wide of the far post.

Chelsea were forced to play with 10 men for short period midway through the half as Malouda came off, initially to have his leg strapped at the side of the pitch but then making the long walk round to the tunnel.
Anelka eventually replaced his compatriot after 29 minutes. A minute later Schwarzer saved a swerving effort from Drogba with his legs.
Chelsea possession was going astray too often in the Fulham half, Deco in particular suffering a wasteful first half.
On 35 minutes Cech saved from Zamora after Mikel had lost the ball. Fulham were ahead, Chelsea were struggling to get level but the Chelsea keeper was hardly overworked.
On 36 minutes injury struck again - a second early sub needed to replace Alex. Carvalho was back in action for the first time in two months.
In the minutes leading up to the break, Lampard did his best to pull his side back into it, twice forcing saves from the keeper, but the Blues went in at the break still a goal down.
The second half began with a crisp 20-yard volley by Ivanovic which was halted on its way by Anelka. It then took good Fulham defending to take the ball off the toes of Lampard as Joe Cole teed up a shot.
The start to the half was good and it got even better just four minutes in when the sheer presence of Drogba forced centre-back Hughes and keeper Schwarzer to challenge each other for a bouncing ball. It fell perfectly to Lampard to slam in from 10 yards - his second goal of the Christmas fixtures.
It was now all Chelsea, an Anelka drive blocked and then Drogba smashing over the bar after he was found by a peach of a Lampard pass over the defence.
On the hour Bosingwa swung a cross over to Lampard's head but he was both off-target and offside.
Four minutes later Lampard played on to Joe Cole but the volleyed shot was struck into the keeper's chest. A second Cole effort soon after was spilled by Schwarzer but it was cleared before Anelka could pounce.
Only Liverpool and Fulham have conceded less than Fulham this season but the Blues were looking good for a winner. The home side fought back briefly with a well-struck Pantsil effort that flew a couple of yards wide.
On 71 minutes Kalou came on for Joe Cole just as Lampard was preparing himself for the 25 yard free kick that broke the Cottagers' resistance. Struck low past the wall, it swerved away from Schwarzer and although the keeper should have done better, it was still a fine strike - reminiscent of Lampard's free-kick at the same Putney End in the 4-1 win of 2004.
Fulham made two substitution and Drogba was booked for a handball as the game entered its final 10 minutes but nothing looked likely to change the tide of this game by the river.
Cech had remained untroubled for the second half until a corner was conceded with 88 minutes on the clock. Played deep by Davies, Dempsey met it with his head to divert it inside the far post to Chelsea's despair.
Bosingwa was the game's second booking in stoppage time but not before first Ashley Cole had a fierce shot saved and then Lampard's follow-up was blocked in front of the net to deny him a hat-trick in stoppage time.
Chelsea (4-3-3): Cech; Bosingwa, Alex (Carvalho 35), Ivanovic, A Cole; Deco, Mikel, Lampard (c), J Cole (Kalou 71), Drogba, Malouda (Anelka 29).
Scorer Lampard 49, 73.
Booked Drogba 81, Bosingwa 90+1.
Fulham (4-4-2): Schwarzer; Paintsil, Hughes, Hangeland, Konchesky; Dempsey, Murphy (c) (Baird 90+2), Etuhu (Andreasen 78), Davies; Zamora (Nevland 77), Johnson.
Scorer Dempsey 10, 89.
Booked Dempsey 90
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