Essien had returned to Jose Mourinho's side after injury, with John Obi Mikel also starting in midfield, while the home side welcomed back Fernando Morientes to partner David Villa in attack.
The opening minutes saw little action in either penalty area, however, with half an hour played the home side woke up and following a quick counter Morientes thundered a left-foot strike against an upright from the edge of the area with Petr Cech stranded.
Two minutes later Morientes made no mistake, firing home left-footed from six yards after Joaquin's ball in from the right had been allowed to drift over towards the far post.
It was almost 2-0 two minutes further on as Villa's ball from the left reached the far post and Ashley Cole made a superb block from Morientes' shot.
Five minutes before the break Didier Drogba almost snatched an equaliser, meeting Cole's cross from the left with a perfect header, but Santiago Canizares made an amazing save high to his left to preserve his side's lead.
Mourinho brought on Joe Cole at the interval to shake things up and seven minutes later the tie was level at 2-2.
Drogba was crowded out in the area following Essien's cross from the right, but Andriy Shevchenko was on hand to drive the ball home from close range.
That setback seemed to totally unsettle Valencia and the visitors began to run the show, with Drogba drawing a save from Canizares midway through the half with a low 20-yard effort.
Substitute Miguel Angel Angulo threatened 11 minutes from time, before Canizares produced his second stunning save of the game with six minutes left, pushing the ball up and over the crossbar after Michael Ballack had headed Frank Lampard's free-kick down towards the far corner of the net.
That looked like being enough to send the tie into extra-time, but, in stoppage time, Joe Cole turned away from his marker in midfield and fed Shevchenko, who in turn found Essien, who advanced and drove a low shot past Canizares at his near post to snatch a dramatic victory.