Kevin Campbell squeezed Everton closer to the Champions League with a vital first-half winner at The Hawthorns.
David Moyes' men came from behind to inflict a seventh-consecutive defeat on a West Brom team resigned to an immediate return to the Nationwide League.
Like so many other times during this trying season Gary Megson's men emerged with nothing despite having had most of the chances and possession.
But one crumb of comfort they can take after a lively approach towards prolonging the inevitable is that other results conspired to allow them to hang onto their Premiership status for at least another seven days.
Igor Balis had given the home side a deserved 18th-minute lead from the penalty spot but they paid for a catalogue of missed chances when David Weir headed the equaliser five minutes later.
A rare mistake by Russell Hoult resulted in Campbell sweeping Everton into a barely-deserved lead on the stroke of half-time after Daniele Dichio, Larus Sigurdsson, Andy Johnson and Ronnie Wallwork had all missed glorious chances to fire the home side's improbable survival fight.
At least Albion came out fighting and for much of the first period it was hardly obvious which of these sides was the one apparently doomed to the drop.
After a bright start Dichio rattled the crossbar with his fifth-minute header from Lee Hughes' cross.
Wayne Rooney - surprisingly kept in the starting line-up despite the growing pressure following his international debut - threatened to cause problems when he poked a 13th minute effort over the crossbar.
But for the most part he was well shackled by Sigurdsson and would only have a couple more chances of note in the rest of the game.
Derek McInnes and Jason Koumas both tested visiting goalkeeper Richard Wright before Albion took their deserved 18th minute lead.
Alan Stubbs handled Sean Gregan's long ball in the box under pressure from Dichio and Balis coolly stepped up to send his resulting spot-kick into the net to Wright's left.
But Everton were level five minutes later when Mark Pembridge's dangerous corner caught out the normally unflappable Hoult and Weir flicked the ball home.
Campbell was ruled offside after converting Joseph Yobo's deep cross with a fine header moments later but from then on it was Albion who looked most likely to regain the lead.
Hughes cut into the box and squeezed between Stubbs and Weir before crossing for Johnson, who somehow contrived to stroke his low shot wide of Wright's right-hand post from point-blank range.
Rooney almost caught out the stranded Hoult at the other end but Albion continued to press forward in a lively half.
Superb work between Balis and Hughes in the 41st minute resulted in a deep, low cross with which Wallwork was inches from connecting in front of goal.
But as has happened so many times this season Albion paid a heavy price for their profligacy in front of goal.
Weir missed a free four-yard header from another Pembridge corner before Hoult spilled a cross and allowed Rooney to retrieve the ball from the byline and cue up Campbell for one of the simplest goals of his career.
Albion were still looking the brighter side but the clear-cut chances were much less in evidence in the second half.
Hughes and Dichio both came close while Rooney hit a 20-yard shot wide for the visitors.
In the end Everton held onto their victory with relative ease but Albion did not let up the fight until the final whistle. Everton might have loftier aspirations than Albion, but Real Madrid will hardly be quaking in their boots.
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