Everton and Arsenal shared a goalless draw as incoming Toffees manager Carlo Ancelotti and Gunners head coach Mikel Arteta watched on from the stands at Goodison Park.
In a first half of few chances, Richarlison had an effort blocked by Bukayo Saka, while Gabriel Martinelli shot wide of the post for Arsenal.
Jordan Pickford denied Pierre-Emerick Aubameyang early in the second half before Lucas Torreira superbly blocked a Dominic Calvert-Lewin effort at the other end.
Everton move up one spot to 15th, on 19 points, with Duncan Ferguson ending his stint as caretaker manager unbeaten in three Premier League matches.
Arsenal are four points above in 11th ahead of Arteta's first fixture in the dugout on Boxing Day.
See: Everton report | Arsenal report
Next fixtures
Everton: 26 Dec v Burnley (H)
Arsenal: 26 Dec v AFC Bournemouth (A)
Referee: Kevin Friend. Assistants: Adrian Holmes, Mark Scholes. Fourth official: Lee Mason. VAR: Graham Scott. Assistant VAR: Andy Halliday.
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