As if to reminder Palace of the danger of a one-goal lead, on 66 minutes, a long ball broke kindly for Carlos Alcaraz to charge through into the box. From a tight angle, at pace, the midfielder fired a rising shot goalwards – but Henderson sprung high to turn it over the bar.
But for all of Palace’s positive play, there remained just one goal in it – and a chipped ball forwards toward Tim Iroegbunam saw Lacroix second to it inside the box, the Everton man drawing a foul.
Iliman Ndiaye stepped up and sent Henderson the wrong way for an equaliser against the run of play.
Everton tails were certainly up, and home voices lifted – but Palace, to their credit, looked like they would defy any inevitable fatigue to battle to a fully-merited point.
That was until a cruel twist three minutes into stoppage time. Ndiaye managed to dig out a cross from the right, Beto headed down, and Henderson made a superb save at point-blank range.
Muñoz, unsighted, spun and attempted to clear, the ball cannoning off Grealish and into the roof of the net.
Despite a succession of late long balls into the box, Palace could not pick up any points on Merseyside, their run unbeaten just short of the six-month mark – which, when reflected upon by generations to come, was quite the feat in itself, despite today’s bitter taste of defeat.
Everton: Pickford (GK), O’Brien, Tarkowski, Keane (Iroegbunam, 65), Mykolenko, Gana, Garner, Dibling (Alcaraz, HT), Ndiaye (Coleman, 90+10), Grealish, Barry (Beto, HT).
Subs: Travers (GK), King, Patterson, McNeil, Aznou.
Palace: Henderson (GK), Muñoz, Richards, Lacroix, Guéhi, Mitchell, Kamada (Lerma, 81), Wharton, Pino (Devenny, 88), Sarr (Uche, 89), Mateta (Nketiah, 70).
Subs: Benítez (GK), Canvot, Sosa, Cardines, Hughes.
As It Happened