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The hosts took the lead in spectacular fashion in the eighth minute when a Shaun Maloney corner found Ramis on the edge of the area, allowing the defender to volley past Jussi Jaaskelainen powerfully.
Jaaskelainen had to be alert to keep out Maloney's long-range strike shortly after as the Latics looked to take advantage of the away side's slow start.
West Ham had numerous chances to equalise before the break with both Matt Jarvis and Andy Carroll guilty of being wasteful in front of goal.
The Hammers were punished for not taking their chances after the interval as Wigan doubled their lead through McArthur.
Maloney capitalised on a poor clearance from Jaaskelainen and picked out McArthur, who easily slotted in his side's second of the game.
Sam Allardyce brought on Carlton Cole to join fellow substitute Modibo Maiga and Andy Carroll in attack but Wigan's defence continued to frustrate their opponents.
The visitors did find a late goal through James Tomkins but Wigan managed to survive and claim the three points.