The pressure on Everton manager Ronald Koeman increased as his side dropped into the relegation zone after a 5-2 defeat to Arsenal at Goodison Park.
Arsenal made by far the brighter start against opponents whose lack of confidence was soon apparent, and the visitors were almost ahead after only four minutes.
The chance came when Alexis Sanchez found Mesut Ozil, who freed Aaron Ramsey for a strike that was well stopped by home keeper Jordan Pickford.
Seconds later Pickford dashed out to close down Sanchez as the Chile international found space near the byline, and Arsenal fashioned a third opportunity after only 11 minutes when Hector Bellerin crossed for Alexandre Lacazette to force Pickford into further action.
But that early dominance was to prove in vain when, a minute later, Everton took the lead through a superb goal from Wayne Rooney.
Granit Xhaka was closed down quickly inside his own half by Idrissa Gueye, with Rooney picking up possession to curl a stylish finish past Petr Cech from the edge of the area.
The goal rattled Arsenal, who were almost two down when Petr Cech was challenged by Dominic Calvert-Lewin but saw the ball run to safety, but the Gunners levelled with five minutes left until the break when Pickford stopped a low shot from Xhaka but Nacho Monreal smashed in the rebound.
Arsenal began the second half on the front foot and took the lead in style after 53 minutes as Sanchez swung in a fine cross from the left and Ozil, arriving in the penalty area, glanced a deft header past Pickford.
And Everton's hopes of finding a way back into the game were soon hit when Gueye lunged in late on Xhaka to pick up a second yellow card as the under-fire Koeman looked on in frustration from the touchline.
With 74 minutes played, Koeman and Everton were condemned to another defeat as Arsenal sliced through again, Ozil finding space and squaring for Alexandre Lacazette to crash in an emphatic finish.
Arsenal boss Arsene Wenger brought on Jack Wilshere for his first Premier League appearance for the club since last August, the midfielder replacing Lacazette for the last 12 minutes, and his side almost added a fourth when Xhaka's strike hit the bar.
They did find one after 90 minutes when Wilshere slid the ball through to Ramsey, who placed a neat finish beyond the demoralised Pickford.
Everton pulled one back when Oumar Niasse struck after a mix-up between Cech and Monreal in stoppage time, but there was still time for Arsenal to add a fifth through a fine angled strike from Sanchez.