Ancelotti's appointment was confirmed by Everton just over an hour prior to kick-off and the former Real Madrid and Chelsea head coach will likely have been happier than new Gunners boss Arteta by what he saw.
Interim Arsenal boss Freddie Ljungberg named a young starting line-up, leaving Mesut Ozil out of his squad entirely, but they failed to provide service to isolated captain Pierre-Emerick Aubameyang.
Ljungberg's Everton counterpart Duncan Ferguson, who had secured four points from two games against Chelsea and Manchester United, will now step aside as Arteta and Ancelotti take charge for the next round of league games on December 26.
Alex Iwobi's first appearance against Arsenal since leaving the club lasted only 10 minutes before he had to be taken off due to an apparent hamstring injury.
The points are shared on Merseyside#EVEARS— Arsenal (@Arsenal) December 21, 2019
A Gylfi Sigurdsson free-kick into the side-netting was the closest either side came to working a goalkeeper during a woeful first half in which Arsenal mustered a single shot.
Jordan Pickford made an unconventional save to keep out Aubameyang's close-range shot after the restart, the striker then sending a tame effort at the goalkeeper.
Dominic Calvert-Lewin's blocked shot came from a rare Everton foray forward as Arsenal largely controlled the second period without incision.
Ferguson's spell ended with him withdrawing a substitute for the second game running, Iwobi's early replacement Cenk Tosun making way for Moise Kean, who suffered the same fate last weekend when he was hauled off at Old Trafford after playing just 19 minutes.
What does it mean? Poor game offers new managers food for thought
Arteta and Ancelotti could have been forgiven for reconsidering their decisions to sign long-term contracts at their new clubs as they watched a game almost entirely lacking quality, which leaves Arsenal ninth and Everton 15th in the table.
Both men will hope funds are available to sign squad reinforcements during the January transfer window. They will need new arrivals if they are to inspire turnarounds at two under-performing clubs.
Everton defence offers Ancelotti a platform
A first clean sheet in the Premier League for over two months could not have come at a better time for the Toffees, who have struggled at both ends of the pitch this season.
Yerry Mina was particularly impressive and Mason Holgate's potential is finally beginning to be realised.
Though Everton offered little threat, Arsenal also kept their first clean sheet since October in any competition.
Saka struggles in unfamiliar role
Injuries to Kieran Tierney and Sead Kolasinac meant Bukayo Saka was pressed into action at left-back by Ljungberg.
The teenage forward struggled with his positioning throughout and could have been sent off after a string of poor challenges.
Arteta's first game in charge of Arsenal comes away to Bournemouth on Boxing Day, while Carlo Ancelotti's bow will be at home to Burnley.