McClean claimed the assist for the opening goal on 10 minutes, when his cross from the left was knocked past his own goalkeeper by Cooper, seemingly under little pressure.
The second goal was more spectactular, McClean taking delivery of a nice ball from Don Cowie to smash into the back of the net, securing Wigan’s first win under Malky Mackay at the sixth attempt.
Leeds bossed the majority of the game but found Wigan’s new-look back-five formation – plus goalkeeper Scott Carson – in unbeatable mood.
After Leeds started the busier of the two sides, the visitors took the lead with their first attack on goal.
McClean did all the damage down the left-hand side, and his cross was bundled into his own net by an unsuspecting Cooper.
Stung into action, Leeds raised their game and Wigan’s rearguard had to be alert to preserve the advantage.
Mirco Antenucci was seeing plenty of the ball down the left, and one cross was headed goalwards by Billy Sharp only for Scott Carson to flick the ball over.
Carson then had to be alert to cut out an Antenucci cross aimed at Sharp, before Tommaso Bianchi fired wide of the mark.
Marc-Antoine Fortune almost made it 2-0 just before the break only to be denied by the legs of Marco Silvestri.
Leeds made a double change at the interval, throwing on Rodolph Austin and Steve Morison.
And the big striker was the focal point for much of what followed as Leeds threw everything at the visitors.
Antenucci fired wide before Giuseppe Bellusci saw a shot tipped over by an increasingly busy Carson.
Wigan were looking dangerous on the counter and McClean’s shot was parried by Silvestri and helped away by Bellusci with Cowie sniffing around for scraps.
Ivan Ramis did likewise at the other end as Morison tried to play in Sharp, with the substitute then seeing a header tipped over well by Carson.
Leeds knew it was not their day when Sam Byram somehow scooped over the bar from a yard.
Then McClean, who had just tested Silvestri with a low strike, sealed the win with 10 minutes to go with a rasping drive from close range.