Dempsey, who humiliated Green 112 days ago at the World Cup, beat the England stopper from 12 yards with a volley after 32 minutes as Fulham ended a bruising first-half 1-0 up.
Any hopes of a first league away win in 13 months were dashed by Frederic Piquionne, who leapt unmarked in the box to nod past Mark Schwarzer.
Wigan's win over Wolves, and Everton's first win of the season at Birmingham mean the Hammers dropped back to the bottom of the pile despite extending their unbeaten run in all competitions to four matches.
Hammers boss Avram Grant was dealt an early blow with the news that Kieron Dyer had failed to recover from a stomach upset.
Fulham boss Mark Hughes, whose side had enjoyed a six-match unbeaten run before kick-off, paired Dempsey in attack with fellow American Eddie Johnson.
Green was coming face to face with Dempsey for the first time since his embarrassing blunder in Rustenburg and the American wasted little time in trying to test the goalkeeper from long range - but his weak effort curled wide.
The shot came moments after Dempsey was hauled down on the halfway line by Danny Gabbidon, who entered referee Andre Marriner's notebook for the challenge.
Piquionne, preferred to England striker Carlton Cole after scoring last week's winner, then drew a goal-line clearance from Carlos Salcido with a powerful header.
It was Fulham, though, who had most of the early possession. Duff, who had earlier received treatment for a cut above the eye, fired just wide from 25 yards in the 10th minute.
West Ham started to hit back and Schwarzer had to be quick off his line to beat Piquionne to the ball after Mark Noble had split the Fulham back line.
Dempsey was left with a large bump near his eye after an aerial challenge with Manuel da Costa. He complained he had been elbowed by the defender but Marriner allowed play to continue.
Danny Murphy's lofted ball over the top set Johnson free but he went down under pressure in the box from Lars Jacobsen - but Marriner failed to give a penalty, much to the annoyance of Hughes.
A smile could be seen on the Welshman's face moments later when Dempsey was played in over the top by Simon Davies, before he despatched a left-foot volley past Green from 12 yards to put Fulham 1-0 up.
Dickson Etuhu picked up a booking for a late challenge on Scott Parker, who had received a yellow a few minutes earlier for a clumsy hack on Dempsey. The American then came close to doubling Fulham's advantage soon after the break when his curling shot bounced on top of the bar.
Slack marking cost Fulham after 50 minutes as West Ham drew level through Piquionne's header.
Brede Hangeland's misplaced pass was picked up by Luis Boa Morte, who laid the ball down the right flank to Obinna. The Nigerian's cross was at the perfect height for the unmarked Piquionne, who made no mistake from six yards for his third goal in three games.
Dempsey then outmuscled Da Costa and Gabbidon to break into the Hammers' box but Green came to the rescue by rushing out to bravely snatch the ball from the forward's feet.
Hammers captain Matthew Upson became the fourth player to receive a booking when he mistimed a sliding challenge on Dempsey just after the hour.
Cole, who has failed to find the net for West Ham so far this season, came on for Barrera with little over 20 minutes to go while Fulham brought on Zoltan Gera for Duff, who limped off holding his left leg.
Dempsey then came close to putting Fulham ahead when he glanced a header just wide of Green's right-hand post from Gera's cross.
Diomansy Kamara came on to replace the ineffective Johnson with 15 minutes left as both sides struggled to take hold of the game.
Green then beat away a difficult Simon Davies shot with five minutes left.
The England stopper came to his side's rescue shortly after when he reacted well to save from Etuhu's header.
Both sides were going all out for victory in the last few minutes.
Kamara failed to take advantage of a golden chance to grab the win in injury-time when he was played in behind the back four but missed the target with a wild effort.
Salcido's body check on Boa Morte angered Grant, who marched 20 yards out of his technical area to remonstrate with the referee in the dying seconds.
The Hammers pushed right until the end for a winner but fell short, causing Grant's side to drop to the bottom of the table.