Jermaine Beckford equalised ten minutes into the second half, but Koumas sealed victory with a deflected free-kick on 69 minutes.
Dennis Wise said: "I thought we put up a good fight. We've done okay performance-wise in pre-season. We're getting together and I'm pleased with them."
Leeds: (442): S Loach 7 — S Gardiner 7, B Parker 6, R Marques 7, E Lewis 6 — D Prutton 7 (sub: R Bayly 75min, 6), J Douglas 6 (sub: C Weston 75, 6), A Thompson 8 (sub: J Howson, 75, 6), I Westlake 6 (sub: S Carole, 75, 7) — T Kandol 7 (sub: T Elliott 75, 6), J Beckford 7.
Substitutes Unused: L Coritzo, F Delph.
Wigan: (4-4-2): C Kirkland 7 — M Melchiot 6, T Bramble 6, A Granquist 7, K Kilbane 7 — A Valencia 6, M Brown 7 (sub: T Cywka 80, 6), D Landzaat 6 (sub: P Scharner, 46, 7), J Koumas 8 (sub: D Cotterill, 78, 6) — J Agahowa 6 (sub: A Sibierski, 46, 7), E Heskey 6 (sub: C Folan 46, 6).
Substitutes Unused: M Pollitt, P Moore, L Montrose.
Referee S Mathieson Attendance 7,469
Player ratings supplied by The Times newspaper.