Arouna Kone struck twice in two minutes at the end of the first half to give Roberto Martinez's side the advantage.
Maynor Figueroa added a third early in the second half, and when Pavel Pogrebnyak was sent off on 55 minutes, Reading's slim hopes all but disappeared.
The two clubs' situation led to a tense first half with chances at a premium, although Wigan started brightly, with Franco Di Santo forcing Adam Federici into a fine save low to his right after just five minutes.
Reading asserted themselves for the bulk of the first period, but their pressure was not translated into meaningful chances, with lone striker Pogrebnyak shackled by Paul Scharner.
The home side's Australian goalkeeper maintained the status quo with another good save after Wigan upped their game, punching away Kone's shot from close range after the striker had done well to get the ball out from under his feet.
And this served as a prelude to a fine end to the half for Wigan and their top scorer, who turned a Figueroa effort at a corner into the net with his chest.
Barely a minute later Wigan doubled their lead when Kone latched onto a fine Beausejour pass that bisected the home defence, and then coolly chipped the advancing Federici as the Reading keeper closed in on the Ivorian.
Brian McDermott introduced Adam Le Fondre at the break, hoping the striker would make another effective contribution from off the bench.
However the game was put even further from the Royals' reach within three minutes of the restart, Figueroa racing onto a pass from Di Santo before placing the ball home through Federici's legs.
Even worse was to follow for the home side on 55 minutes, when Pogrebnyak was shown a straight red card. The striker lashed out a foot in frustration at Figueroa having lost the ball, and referee Phil Dowd showed little hesitation in dismissing the Russian.
Federici then clawed away a Figueroa shot from 25 yards out high to his right, and Jordi Gomez, who hit a hat trick in the reverse fixture earlier in the season, saw his stabbed effort punched to safety.
Wigan were in complete control for the remainder of the game, and with Aston Villa losing at Arsenal the perennial Premier League strugglers climbed out of the relegation zone.