The honeymoon for West Ham's new Icelandic owners is over after Everton's Leon Osman and James Vaughan scored goals to push Alan Pardew's side back down the table to 17th.
The momentum from last week's victory proved short lived as the trip to Merseyside was a disappointing one.
However, the home side now jump to seventh after Leon Osman scored his first goal of the season to mark his 100th appearance for the club in style before substitute James Vaughan rounded out the scoring to have the Hammers just a point above the drop zone.
One piece of good news for West Ham was the performance of striker Carlos Tevez who looks to be finally settling into English football.
The former Corinthians striker was a constant threat to the home side in a one-sided first half, drawing a fine save from Everton keeper Tim Howard and setting up Lee Bowyer with a glorious chance to open the scoring in the 18th minute.
Gliding easily past the challenge of Joleon Lescott, Tevez pulled the ball back to Bowyer who stared in disbelief as Howard reacted superbly to turn the midfielder's first time shot over the bar.
West Ham's superiority was confirmed by their haul of ten corners inside the first half hour but Everton finally began to make an impression through Andy van der Meyde and Andy Johnson who had both been hurriedly brought into the line-up after training ground injuries to Phil Neville and Mikel Arteta a day earlier.
Van der Meyde is another player who has struggled to make an impression since moving to England but he marked his first Premiership start of the season with a series of quality crosses deserved more reward.
Relieved at having reached half-time on level terms, Everton finally began to take control of the game and West Ham were forced to rue their earlier missed opportunities when the home side went ahead in the 52nd minute.
Striker James Beattie created the chance by chasing down a long ball that appeared to be going out and delivering a threatening cross that Jonathan Spector could only half-clear towards Osman on the edge of the box.
The youngster showed impressive composure to bring the ball down on his chest before volleying past Green before Vaughan ended West Ham hopes in the final seconds.