Arouna Kone's double at the end of the first half was quickly followed by a rare Maynor Figueroa goal after the re-start to grab just a second win in 14 Premier League games for the visitors.
Reading's afternoon deteriorated rapidly and when Pavel Pogrebnyak was given a straight red on 55 minutes for a reckless challenge on Figueroa there was no way back.
There had been little evidence of the fireworks to come at the end of the first half as both sides provided only rare glimpses that they were aware victory could move them outside the bottom three.
Reading controlled possession for the majority of it but were indebted to a pair of Adam Federici saves before they fell behind. The Australian was first called into action after just four minutes when Franco Di Santo expertly rolled Jem Karacan in midfield before firing a low shot that Federici just turned wide.
Paul Scharner kept the scores level with a perfectly-timed sliding challenge to deny Pogrebnyak as he looked certain to turn in a low Kebe cross. It was Reading's last chance before the game was stolen away from them in spectacular style.
Federici had made a second good save, reacting well to Kone's poked shot, before he was left exposed by poor marking for the opener soon after. Gary Caldwell was completely unchecked from a corner and while he made a hash of the chance, the ball bounced to Figueroa whose shot was going in before taking a deflection off Kone's back near the line.
Kone knew little about his opener but his second was a goal to remember. After Sean Morrison lost the ball Jean Beausejour delivered a defence-splitting run to find Kone's run. The striker still had the onrushing Federici to beat but nervelessly chipped his shot over him and into the net.
It was the last action of the half and the home fans responded with boos at the whistle. McDermott responded by bringing top-scorer Adam Le Fondre on at the break. But Figueroa made it 3-0 moments after the re-start as he was allowed to exchange passes with Di Santo and, with no defender around, fire his shot through the legs of Federici.
There was yet more punishment waiting for Reading, however, as Pogrebnyak was given his marching orders. The striker recklessly challenged Figueroa as he burst forward, stamping down on the defender's ankle, to prompt a straight red from referee Phil Dowd. Wigan then took complete charge and it was surprising only that a fourth did not arrive.