Ancelotti was confirmed as the Toffees new boss on the morning of the match, 24 hours after Arteta took charge of Arsenal, AFP reported.
Both new managers were in the stands with Duncan Ferguson and Freddie Ljungberg in temporary charge for the final time.
And the lack of confidence of two sides struggling at the wrong end of the table was obvious in a match completely devoid of quality.
A point edges Arsenal into ninth, but the Gunners have now won just once in their last 13 games in all competitions.
Everton move up to 15th, but is only four points clear of the relegation zone.
Ferguson's role in Everton's impressive victory over Chelsea and draw at Manchester United in its last two league games was enough to ensure the temperamental Scot a role in Ancelotti's backroom staff.
However, there was a dramatic dip in his side's energy levels as it looked jaded after a League Cup quarterfinal defeat on penalties to Leicester in midweek.
Ljungberg named a youthful Arsenal side with 19-year-old Emile Smith Rowe starting for the first time in the Premier League alongside Reiss Nelson and teenagers Gabriel Martinelli and Bukayo Saka.
Mesut Ozil, Alexandre Lacazette and Nicolas Pepe were among those left out by the Swede, who won just one of his six matches in caretaker charge.
Martinelli had the best chance of a first half that ended without a single shot on target from either side when he sliced wide from Lucas Torreira's fine through ball.
Substituting a substitute
Arsenal was the better side after the break as it finally got top scorer Pierre-Emerick Aubameyang into the game.
The Gunners' captain was denied by a fine save from Jordan Pickford as he pounced on Callum Chambers's flick on from a corner. Then Aubameyang fired too close to the England number one with his next effort.
Ljungberg's final decision of his caretaker spell was a brave one as he replaced Aubameyang 13 minutes from time as Lacazette was finally called on from the bench.
However, the focus was again snatched by Ferguson's substitutions as for the second straight week he replaced a substitute.
Moise Kean was the victim of his impatience at Old Trafford last weekend as the Italian international was hooked after just 18 minutes.
This time it was Kean who was introduced for Cenk Tosun, who had come on early in the game for the injured Alex Iwobi.
But Kean could not make himself a hero by scoring his first Everton goal as Arsenal held out for a first clean sheet in 15 games.