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The Ivory Coast forward netted a brace in the FA Cup win over Huddersfield Town last week and continued his fine form in the opening 45 minutes at the Madjeski Stadium.
The Royals stopper had earlier kept the scores goalless with a low stop from Franco di Santo's powerful drive.
However, he was helpless to prevent the fortunate opener from Kone, who netted a second just a minute after breaking the deadlock.
He collected a pass from Figueroa 35 yards out, charged past the Reading defence and dinked the ball over Federici to give Wigan a crucial advantage in the bottom-of-the-table clash.