© PA Photos
Kone netted twice in the minutes prior to the break at the Madjeski Stadium, while Maynor Figueroa, creator of both of the Ivorian's goals, netted a third just after the interval.
Reading have produced several second-half comebacks in recent weeks but a Pavel Pogrebnyak red card ended their slim chances of a repeat performance.
On 44 minutes, Figueroa directed a header goalwards which found the net via a deflection off Kone, who dinked Wigan two clear.
The Latics' forward collected a Figueroa pass 35 yards out, travelled with the ball past a pair of Reading defenders before cleverly chipping Federici just ninety seconds after bagging his first.
Honduran Figueroa then ended a two-year goal drought when he combined with Di Santo before stroking the ball through Federici.
Pogrebnyak was sent off for a lunge on the Latics defender to compound a miserable afternoon for Reading, who drop into the bottom three in place of Wigan, who climb to 17th.