Everton had staged a superb second-half comeback through substitute Thierno Barry and Jake O'Brien as they eyed a famous victory.
But they could not hold on as David Moyes' long wait to secure a league victory over Pep Guardiola continued – he has now gone 17 meetings against the Spaniard without claiming three points and claimed just three draws in that run.
The Scot's side were all over Manchester City in the second half and with better finishing could have been out of sight, before they conceded to Doku's stunning last-gasp equaliser.
Iliman Ndiaye ran the City backline ragged and forced Gianluigi Donnarumma into a full-stretch save low down – then the Senegal winger had an even better chance four minutes later when Marc Guehi and Matheus Nunes got in each other's way, but he was denied by the Italy keeper again.
Barry's equaliser was awarded as the offside had been reset by Guehi deemed to be in controlled possession of the ball with no pressure from the Everton striker, who took full advantage off his error to equalise.
The Frenchman scored again after O'Brien's thumping header and Everton looked set for all three points until they conceded a goal past the 90th minute for a third consecutive game.
But Mikel Arteta and Arsenal will surely not mind that too much – as this result still puts them firmly in the driver’s seat for the title with just three games remaining.
