The Serbia international had 10 attempts but could not add to his tally of nine goals this season as Everton hung on for a point.
Fulham, who could have moved level on points with local rivals Chelsea had they won, dominated the game but Everton were disciplined as they recorded a first clean sheet of the season.
Marco Silva's Fulham moved into seventh spot with 19 points while Everton are 12th with 14 points.
Everton were indebted to keeper Jordan Pickford who made several saves early on as Fulham started fast.
Everton striker Dominic Calvert-Lewin was also needed in defence to make a clearing header off the line.
Mitrovic racked up the efforts on goal, lashing one effort over the bar, and was in the thick of the action.
He was perhaps lucky to escape a red card for a first-half tackle on Idrissa Gueye in which he caught the Everton player on the shin.
"It was a red card for Mitrovic, I have nothing against him but he knew, he put his arm up straight away," Everton manager Frank Lampard said.
"VAR is there to deal with these things."
On his side's new-found resilience, Lampard said: "Last year we would lose that game so there is progress, but I want more."
Fulham's Silva said it had been a frustrating night as his side failed to score at home for the first time this season.
"It's difficult to believe, really. We did almost everything well. Everton played a direct game, we knew that, and they created some moments but we are always on the front foot.
"Mitro will score next time."