Wayne Rooney completed his first Everton hat-trick with a stunning effort from inside his own half as manager-in-waiting Sam Allardyce watched a 4-0 Premier League victory over West Ham from the stands at Goodison Park.
Rooney produced the sublime first-time long-range effort to complete his treble after heading in on the follow-up after his penalty was saved by Joe Hart and slotting home his second 10 minutes later.
Jordan Pickford saved Manuel Lanzini's spot-kick and Ashley Williams then added a header.
It all made for a thoroughly miserable night for former Everton boss Moyes and a hugely satisfying one for Toffees caretaker manager David Unsworth, who celebrated only the second win of his temporary stint.
Allardyce, sat alongside Everton's major shareholder Farhad Moshiri and chairman Bill Kenwright, will surely have taken great encouragement from what he saw hours after the club had announced he was to finalise terms on becoming their new manager.
Raheem Sterling scored a dramatic winner as Manchester City maintained their winning run with a last-gasp 2-1 defeat of Southampton.
The England forward - who netted a late clincher at Huddersfield on Sunday - curled home a superb injury-time strike for the leaders at the Etihad Stadium.
Saints had looked set to become the first team to deny City a victory since August when Oriol Romeu cancelled out Kevin De Bruyne's deflected free-kick.
Arsenal strengthened their position in the top four as they made light work of Huddersfield.
The Gunners have now won their last 12 games at the Emirates Stadium and they eased to a 5-0 victory as Mesut Ozil once again starred in front of the home fans.
Alexandre Lacazette gave the hosts the perfect start with his seventh goal of the season and, although the Terriers rallied, they were blown away in the second half as Olivier Giroud, Alexis Sanchez and Ozil all struck in a four-minute blitz, with Giroud adding another late on.
Head coach Antonio Conte was sent off as Chelsea claimed a fifth league win in six games with a 1-0 defeat of Swansea.
The Italian was dismissed from the touchline for the first time in his Chelsea career by referee Neil Swarbrick after furiously protesting the award of a Swansea goal-kick and watched the second half from the dressing room as Antonio Rudiger's goal proved decisive.
Substitute Mohamed Salah's purple patch continued with two more goals as Liverpool ground out a controversial 3-0 win at Stoke.
Goalkeeper Simon Mignolet was lucky to stay on the pitch with the score at 1-0 after a wild hack at Mame Diouf but referee Martin Atkinson only issued a yellow card.
The official had already angered the hosts with Sadio Mane's opener but there was no doubt about Salah's two late strikes.
Bournemouth boss Eddie Howe endured a miserable 40th birthday as goals from Chris Wood (37) and Robbie Brady (65) gave his former club Burnley a 2-1 win at the Vitality Stadium, with Josh King (79) replying for the hosts.