The Cottagers created some brilliant opportunities but the English goalkeeper was spectacular between the sticks.
Aleksandar Mitrovic, who has already netted nine goals this season, was twice denied by the 28-year-old. He also denied Willian and Harrison Reed.
Fulham had six shots on target, but Everton still earned a clean sheet thanks to Pickford’s string of superb saves.
Everton bag a good result
Everton will be happy to have earned a point at Craven Cottage.
After losing three league matches on the trot, the Toffees bounced back against Crystal Palace last week to claim a superb 3-0 victory.
Frank Lampard’s side didn’t show much attacking intent at Fulham on Saturday, but they were brilliant in defence.
The Cottagers entered the home encounter on the back of successive victories over Aston Villa and Leeds United.
The west London outfit have lost only one game on home soil this season against Newcastle United at the start of this month.
However, the Toffees came away with a point which is encouraging.
James Tarkowski and Conor Coady were brilliant in defence, but Pickford made a huge impact for the Merseyside club.
Following the goalless draw, Everton have moved to 12th in the league standings with 14 points from 13 matches.
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