Avram Grant's Chelsea will be encouraged by the forceful nature of their second-half dominance after a lack-lustre opening period, as they kept the pressure on Manchester United and Arsenal.
Former Internazionale boss Hodgson received a warm welcome from the home fans as he took charge of his first match at Craven Cottage, and it was the hosts who started the brighter as they attempted to impress their new manager, with Diomansy Kamara testing third-choice goalkeeper Hilario with a low shot inside two minutes.
Chelsea recovered from that rocky opening, however, and missed a glorious opportunity on eight minutes when Shaun Wright-Phillips scampered down the right before shooting across Antti Niemi. However, the ball evaded both the onrushing Joe Cole and the far post.
It was to prove an expensive mistake as Fulham went ahead through Murphy's penalty kick two minutes later after Joe Cole had clipped Moritz Volz as the German rushed into the area. Murphy sent Hilario the wrong way to score the first Premier League goal of 2008.
The goal energised Fulham, who looked more confident than any side who have only won two games before the turn of the year deserve to be, while Chelsea appeared short of ideas.
But Grant's men came out for the second half in a much more determined mood and were unlucky not to be awarded a penalty of their own when Dejan Stefanovic appeared to block Wright-Phillips' cross with his arm.
And it took only eight minutes of the second period for them to draw level, Kalou heading forcefully home after Alex had knocked Juliano Belletti's corner back across goal.
On the hour the turnaround was complete when Ballack converted a penalty that he had won himself after Clint Dempsey had pulled at his shirt as they were competing for Belletti's free-kick.
The Germany captain flashed a 30-yard free-kick inches wide shortly after in what was to be the last meaningful action of the game as Chelsea's fans contented themselves with taunting their Fulham counterparts with chants of 'you're going down'.
Unless Hodgson can complete a remarkable transformation in Fulham's fortunes they may be right, while their own team proved they cannot be discounted in the race for the title.