Tommy Spurr gave Blackburn an eighth-minute lead following an error from Scott Carson, but Hanley was then dismissed shortly after the half-hour mark when he caught Nick Powell with a raised arm.
Wigan initially struggled to take advantage of their extra man, but substitute Grant Holt converted a corner with the aid of a deflection from Spurr before Boyce headed home Ben Watson's free-kick in injury time.
Owen Coyle's side climb up to 12th in the Championship as a result, while Blackburn remain ninth.
Spurr’s opener came after Wigan goalkeeper Carson had spilled Tom Cairney’s set-piece delivery.
Hanley’s exit made Blackburn’s task much tougher, however, and Holt drew the hosts level shortly after replacing Thomas Rogne in the 57th minute.
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