The Toffees had been relentless in their pursuit of fourth spot and a gritty victory over Sunderland following a spellbinding win over Arsenal had given them the upper hand.
Last night that was squandered against a Crystal Palace side who were good value for this victory for the majority of the contest an edgy Goodison Park became engulfed with tension.
Everton had reeled off seven successive league wins for the first time since 1985 – a title-winning year – but an eighth victory proved beyond them here.
The defeat left the Toffees a point behind Arsenal in fifth spot with games against both Manchester clubs to come, albeit at home.
Indeed, if they do secure Champions League football from this point they really will have had an impressive season.
Arsenal’s victory over West Ham 24 hours earlier had certainly put the pressure back on the Merseyside club with Roberto Martinez adamant his side would not feel the pressure of the race to beat the Gunners to fourth.
In truth, though, the opposite was true and afterwards he lamented; “It’s a hurtful result. We wanted it so much we stopped being ourselves. Everything that could go wrong did.”
Martinez identified Palace as a team that could dent his side’s hopes, given they came into the game with the division’s fifth best defensive record.
And he responded with an attacking starting line-up as Kevin Mirallas, Ross Barkley and Aiden McGeady came into the side for Leon Osman, James McCarthy and Steven Naismith.
Palace have been the epitome of disciplined and organised since Tony Pulis took over and Everton initially found it difficult to find their way through a midfield packed with yellow shirts.
Direct running became the favoured approach and Barkley’s quick feet saw him denied an early penalty shout while McGeady could only lift his shot over the bar after a jinking run moments later.
Goodison Park seemed surprisingly subdued compared to recent fixtures, and it fell eerily silent after the hosts fell behind shortly before the half-hour mark.
Yannick Bolasie outpaced Leighton Baines and his low centre was parried by Everton goalkeeper Tim Howard into the path of Marouane Chamakh who teed up Jason Puncheon and he found the corner of the net.
The Toffees eventually registered a meaningful attempt on target shortly before half-time when Barkley teed up Romelu Lukaku but a combination of post and the glove of Palace goalkeeper Julian Speroni denied the striker.
Palace served notice of their intent not to sit on their lead after the interval when Joe Ledley brought a smart diving save out of Howard with a rasping shot.
And it came as little surprise that the visitors doubled their advantage from the resulting corner when Scott Dann lost John Stones and powerfully headed into the net.
However, Goodison Park eventually woke from its slumbers on the hour mark when the Toffees pulled one back through Steven Naismith, who bundled the ball home from close range following Mirallas’ persistence.
The goal helped Everton regain their zip and zest as they looked to right the wrongs of the past hour.
But the sucker punch came at the other end when Puncheon shrugged off a number of blue shirts to tee up Jerome and he made no mistake with a confident low finish.
Everton, though, refused to lie down and reduced the deficit again when Kevin Mirallas sprung the offside trap with five minutes left and calmly guided the ball past Speroni.
The referee added six minutes of injury time but despite an aerial bombardment, Everton were unable to find the equaliser.
EVERTON (4-2-3-1): Howard 5; Coleman 6, Stones 7, Distin 6, Baines 5; Barkley 6, Barry 5 (Osman 59; 6); Deulofeu 5 (Naismith 45; 6), Mirallas 7, McGeady 5 (McCarthy 59; 7); Lukaku 7.
CRYSTAL PALACE (4-2-2-1-1): Speroni 7; Mariappa 6 (Parr 68; 6), Dann 7, Delaney 6, Ward 7; Jedinak 7, Ledley 6; Bolasie 8, Puncheon 8; Chamakh 7 (Murray 80;7); Jerome 6 (O’Keefe 76; 6).
Referee: Andre Marriner