Again, the marking was poor as Kompany easily outmanoeuvred Tal Ben Haim before powering an unstoppable header past James.
But Essien, who also criticised for challenges on Bolton's Tal Ben Haim and Arsenal's Lauren, believes the criticism was undeserved.
Chelsea made a double switch with 17 minutes left, sending on Tal Ben Haim and Shaun Wright-Phillips for Ashley Cole and Joe Cole.
Tony Hibbert's hanging cross led to a mix-up between Bolton keeper Jussi Jaaskelainen and Tal Ben Haim and Cahill's athleticism allowed him to fire home an overhead kick from close range.
Valencia dispossessed Tal Ben Haim on the left flank and played the ball into Folan, whose first-time flick allowed Paul Scharner to cross and Heskey bundled the ball home from close range.
Fabio Collocini had to snuff out danger from that pair on 10 minutes, just before Newcastle midfielder Geremi went close with a 25-yard free-kick awarded after Tal Ben Haim hacked down Obafemi Martins.
He has been busy in the market, but mainly at the bargain end as he landed Steve Sidwell from Reading, Bolton's Tal Ben Haim and Bayern Munich striker Claudio Pizarro on free transfers.
Bolton boss Sam Allardyce immediately replaced Ben Haim with Ricardo Gardener to cope with Valencia's pace and the change seemed to do the trick as the visitors drew level six minutes before the interval.
Martins swung a cross in but, as Dunne cleared, the ball deflected off Vincent Kompany and Ben Haim into the path off Ameobi who chested the ball forward and finished awkwardly for his first goal in over two years.
Ben-Haim almost restored parity just after the interval when his powerful header was somewhat fortuitously repelled by the chest of the Everton keeper.
Daniel Cousin put Hull in front, capitalising on Tal Ben-Haim's awful back-pass to flick the ball past Joe Hart, who later went off injured.
Substitute Mame Biram Diouf played the ball one side of Tal Ben-Haim and collected it round the other but then blazed his shot over.
Tal Ben-Haim had a powerful effort blocked by Howard's chest and then Aaron Mokoena's header hit the bar before Everton cleared off the line.
There was little immediate danger when Micah Richards squared the ball across the penalty area to Ben-Haim despite Hull's forwards closing down the space quickly.
Pompey keeper David James saved an early effort from Matt Jarvis and bravely blocked a late Andy Keogh shot, while Tal Ben-Haim threw himself in front of Kevin Doyle's follow-up.
But the popular response to the unilateralist thesis enunciated by such senior figures as Haim Ramon and Shlomo Ben-Ami was too strong for Binyamin Ben-Eliezer, the party's chairman, to withstand.
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