The result sees West Ham return to the bottom of the Premier League table yet they will be satisfied with a point from a full-blooded London derby that was high on energy but low on attacking finesse.
The game may also have laid a few more South Africa 2010 demons to rest for seemingly revitalised Hammers keeper Green, who put in a faultless display and this time could do nothing to prevent his World Cup nemesis Dempsey from opening the scoring.
It was the first chance for the pair to renew rivalries since Dempsey's infamous strike past Green in Rustenburg, and just two minutes were on the clock when the American tried his luck with a speculative 25-yard effort that went well wide.
There were more crunching tackles than chances in a scrappy first 30 minutes, most notably when Manuel Da Costa caught Dempsey with an elbow to the side of the head that went unpunished by referee Andre Marriner.
But the robust American, also the victim of meaty challenges from Danny Gabbidon and Scott Parker and by now sporting a shiny bump by his left eye, dusted himself down to notch an opening goal that Green was powerless to prevent.
Grant surprised by West Ham improvement
Simon Davies' pass took a deflection and looped into the path of Dempsey, who controlled the ball with his chest and cleverly dinked it over Green from 12 yards.
The Hammers were tenacious but toothless, with Carlos Salcido's clearance off the line from Piquionne's early header the only time Mark Schwarzer's goal came under noteworthy threat in the first half.
Fulham boss Mark Hughes was also angered at Marriner's refusal to award the visitors a spot-kick when Eddie Johnson went down under a challenge from Lars Jacobsen.
Within moments of the restart, a Dempsey effort again beat Green but his powerful shot from the edge of the box clipped the top of the crossbar.
Two minutes later, the visitors had relinquished their lead after an uncharacteristic mistake from centre-back Hangeland.
The Norwegian's nonchalant pass out of defence went straight to Luis Boa Morte, who fed Obinna on the right and the Nigerian crossed for Piquionne to head home from close range.
Hughes hopes to convert draws to wins
Fulham had a chance to quickly regain the lead but Green reacted well to dive at the the feet of the impressive Dempsey.
As the game opened up, West Ham's Pablo Barrera and Fulham's Johnson were both guilty of wasting good shooting opportunities, while Etuhu should have done better with a free header.
For the hosts, attacking livewire Obinna enthralled and frustrated the home fans in equal measure with a dizzying mixture of piercing runs and wayward shots.
But it was Fulham who finished the strongest and it fell to Green to preserve West Ham's point and their four-match unbeaten run.
First, the Hammers keeper tipped a fizzing Davies drive around the post, then he made an even better stop to parry Etuhu's powerful header.
There was still time for Fulham to create another gilt-edged chance in injury time but Kamara fired well over from the edge of the box after being sent clean through.
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