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Nikica Jelavic had an early chance to give Everton the lead but the striker was unable to find the target from eight yards as he headed wide.
Reading started to enjoy more of the possession following Everton's early dominance and could have made the breakthrough when a loose ball dropped to Adam Le Fondre, but the striker's effort crashed against the post.
Phil Jagielka was forced off the field with an injury, causing Everton to look nervous in defence and Reading should have taken advantage when Alex Pearce found space inside the area but he stroked his shot wide of the target.
Despite their fragility in defence, Everton took the lead shortly before the interval as Fellaini rose highest to powerfully head Seamus Coleman's cross past Stuart Taylor.