Seamus Coleman's 87th-minute winner gave Everton a 1-0 victory at Crystal Palace, condemning Sam Allardyce to a fourth league defeat in a row.
With the game appearing destined for a stalemate, the Republic of Ireland international rifled a near-post drive past Wayne Hennessey as the Toffees claimed their fourth victory in their last five Premier League outings.
It was a bitter pill for Allardyce - who has earned just one point from his first five league games in charge of Palace - to swallow, with Jeffrey Schlupp down injured as Everton took the lead.
It took Palace 79 minutes to register the first of two shots on target, evidence of the work that lies ahead Allardyce as he looks to secure the Eagles' top-flight status.
Defeat combined with Swansea's win at Liverpool sees Palace drop into the relegation zone. Everton, who have cut the gap to Manchester United to five points, remain seventh.
Ronald Koeman admitted he had no option but to name an unchanged side after the Toffees' demolition of Manchester City last weekend.
To compete with an Everton side brimming with confidence, Allardyce gave Loic Remy his first Premier League start of the season and handed January signing Schlupp his full debut.
Despite having just 20 minutes of top-flight football under his belt this term, Remy set the tone for the hosts, pestering the Everton defence from the first whistle.
It was his strike partner who had to first chance though, Christian Benteke glancing James McArthur's cross onto the bar on seven minutes.
Everton took a quarter of an hour to settle but burst into life when Ross Barkley skipped past three defenders and shot for the top corner, the slightest of deflections turning the ball away.
A minute later Hennessey was called into action again, denying Kevin Mirallas' volley from point-blank range before Barkley's curling effort was tipped over on 20 minutes as the visitors peppered the Palace goal.
When the Toffees finally got the better of Hennessey the post came to Palace's rescue, denying Romelu Lukaku's trickling shot before Barkley's rebound was ruled out for offside.
It wasn't long before Hennessey was called upon again, thwarting Ramiro Funes Mori's thunderous drive on 37 minutes.
Everton continued their dominance into the second half, Barkley flashing an effort across the face of goal after Tom Davies' sublime lofted pass.
Barkley's trickery continued to trouble Palace, the England international curling wide on 56 minutes after evading two defenders on a mazy run.
Unmarked in the area, Lukaku spurned a glorious chance to take the lead shortly before the hour, heading Coleman's cross onto to the roof of the net.
And as the game wore on those misses saw Palace grow in confidence, the Toffees indebted to goalkeeper Joel Robles after he denied Scott Dann's goal-bound header - Palace's first attempt on target.
As Palace piled forward in search of a winner, Schlupp overexerted himself, picking up an injury that would rule him out of the closing stages.
Receiving treatment off the field, the game continued in Schlupp's absence though, and Everton made their man advantage count.
Coleman found space in behind the defensively naïve Chung-Yong Lee and unerringly drilled the ball home as Everton continued their recent upturn with a dramatic late victory.
Player ratings
Crystal Palace: Hennessey (8), Tomkins (6), Delaney (6), Dann (6), Ward (7), Puncheon (6), McArthur (6), Cabaye (6), Schlupp (7), Remy (8), Benteke (6).
Used subs: Townsend (n/a), Lee (5), Ledley (5).
Everton: Robles (7), Holgate (7), Ashley Williams (7), Funes Mori (7), Coleman (8), Davies (6), Barry (6), Barkley (8), Baines (7), Mirallas (6), Lukaku (6).
Used subs: Schneiderlin (5), Jagielka (n/a), Lookman (5).
Man of the Match: Ross Barkley.