Roy Hodgson was dealt a cruel blow in his first game in charge of Fulham after Chelsea bounced back from a goal down to win at Craven Cottage.
Ballack was on the spot for Chelsea
The home side took the lead when Danny Murphy converted a penalty after Joe Cole carelessly tripped Moritz Volz.
Chelsea equalised after the break when Salomon Kalou nodded in Alex's headed pass from Juliano Belletti's corner.
And Michael Ballack grabbed Chelsea's winner from the spot after he had his shirt pulled by Clint Dempsey.
The third-placed Blues had only lost one fixture against their west London rivals in 28 years.
But Chelsea arrived at Craven Cottage deprived of the services of Andriy Shevchenko, Didier Drogba, Frank Lampard, Claude Makelele, John Terry and Petr Cech, which would have given the Fulham faithful and Hodgson the faintest of hope that they could conjure up a shock.
The new boss opted to start with Diomansy Kamara in place of David Healy, and the former West Brom striker almost gave his struggling side a fantastic start when he found enough space in the area to unleash a low drive that keeper Hilario reacted to brilliantly.
Chelsea's pace often unnerved Fulham's defence, although those in blue deputising for their injured team-mates were guilty of some uncharacteristic wayward passing.
When the Chelsea players were in sync with each other they caused Fulham problems.
One sparkling move saw Cole flick the ball into the path of Kalou who in turn attempted to lift the ball over Antti Niemi, but just failed to get enough purchase.
Moments later, the erratic Shaun Wright-Phillips dissected the Fulham defence on the right but rifled his eight-yard angled shot wide of Fulham's right-hand upright.
It was a frantic start to the match which swung the way of Fulham when Volz was adjudged to have been fouled by Cole inside the area.
Referee Mark Halsey pointed to the spot and Murphy took on the responsibility of taking the penalty which was fired low past Hilario.
Defeat would have been a massive blow for Chelsea who would have been left six points adrift of league leaders Arsenal.
Kalou was lively all afternoon
And for the rest of the first half they gave little indication that they would deny 19th-placed Fulham a vital win, with Murphy putting Ballack in the shade in the middle and teenager Elliot Omozusi doing a fine job at the back.
Avram Grant, with a relatively weak bench, replaced the fairly ineffective Steve Sidwell with John Obi Mikel after the break.
The change in personnel and the tinkering of his 4-3-3 formation seemed to do the trick when Kalou equalised eight minutes into the half.
Belletti swung in a corner to the far post that fellow defender Alex headed back into the six-yard area for Kalou to nod in from close range.
That perked up the Blues who then took the lead on the hour mark when referee Halsey awarded his second penalty of the day after penalising Dempsey for his challenge on Ballack.
The Germany international composed himself before picking the same spot as Murphy to give Chelsea the advantage.
With the visitors finally looking like the team 16 places above Fulham, it was now the home side desperately looking to salvage something from the game.
But Fulham could not break through Chelsea's defence and Hodgson was re-introduced to the harsh realities of the Premier League.
Fulham boss Roy Hodgson:
"We got caught by the two set plays which is disappointing because set plays are a big part of the game and it they cost us.
"Some would say the Michael Ballack penalty was a penalty and some would say it wasn't.
"Our attempt to follow the game plan was good as was our committment."
Chelsea boss Avram Grant:
"I'm pleased we've taken 10 points during the Christmas period.
"We started slowly but we seem to do that when we play early in the afternoon. But in the second half we showed a lot of character.
"We scored two goals and I thought we could have scored more."
Fulham: Niemi, Volz (Ki-Hyeon 68), Bocanegra, Stefanovic, Konchesky, Davis (Smertin 70), Davies, Murphy, Omozusi, Dempsey, Kamara (Healy 77).
Subs Not Used: Warner, Kuqi.
Goals: Murphy 10 pen.
Chelsea: Hilario, Belletti, Alex, Ben-Haim, Bridge, Wright-Phillips (Pizarro 88), Sidwell (Obi 46), Essien, Ballack, Joe Cole (Ferreira 90), Kalou.
Subs Not Used: Taylor, Sinclair.
Goals: Kalou 54, Ballack 62 pen.
Ref: Mark Halsey (Lancashire).
BBC Sport Player Rater man of the match: Fulham's Danny Murphy 7.56 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.