City led 1-0 at half-time at the Hill Dickinson Stadium following Doku's sublime curled finish into the top corner in the 43rd minute. In a catastrophic 14-minute spell after the break, substitute Thierno Barry scored twice and Jake O'Brien headed Everton in front to make it 3-1 — the first time Everton had led City in the second half all season.
Erling Haaland immediately clawed one back and Doku completed one of the most dramatic recoveries of the City season with a second curling effort in the final seconds of stoppage time.
The draw leaves City five points behind Arsenal with one game in hand. The title is now firmly in the Gunners' hands.
Speaking after the match, Doku was candid about where City let themselves down.
"First half we played well and created a lot of chances. We know if we don't score those chances it is going to get difficult at the end. Obviously they are at their own stadium, they create chances, they are dangerous, and they scored two goals, but I think we gave them the game. Good that we came back because one point is not bad in games like this."
He acknowledged the second half lapse but refused to let it define the evening.
"Second half we were too sloppy. I think we were winning, so they started to press more, and they are more aggressive as well, and then it's on us to stay calm in those situations. We will see. It feels painful now. There is still a lot of games to go. We lost two points today, but we know that one point can be important at the end."
His message to supporters was straightforward.
"We will keep on fighting. We owe it to ourselves and to our fans."
Doku also reflected on the difficulty of breaking Everton down when their defensive structure was set.
"Difficult because they had players in the box. Whenever we arrive at the byline it is difficult because there is a lot of players there. We scored, then it was more open."
It was Everton manager David Moyes's 17th meeting with Guardiola in management without a victory. City face Brentford on Saturday before a final-day trip to Manchester United that could still determine the destiny of the title.