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After taking an early lead through Gary Teale they saw Gary McSheffrey fire the Sky Blues level with a penalty midway through the first half.
But Nathan Ellington produced a magical second-half volley to move Paul Jewell's men above Ipswich Town in the race for the title.
Coventry handed home debuts to four players as they looked to put a dent in Wigan's promotion hopes.
Marcus Hall was among those four as he started his first match since returning to Highfield Road from Stoke City.
Wigan were on top early on and dangerman Teale handed them the lead after only nine minutes.
He raced onto a lay-off from Jason Roberts and fired home past Ian Bennett from the edge of the area.
The visitors threatened to over-run the Championship strugglers but when Richard Shaw was taken off injured it forced City to reshuffle their team and it paid dividends.
McSheffrey was moved out to the left wing and in the 21st minute he won the home side a penalty that brought them level.
Trevor Benjamin caused havoc with a driving run and when the ball broke to McSheffrey he was upended by Matt Jackson.
Wigan complained that it was a dive but McSheffrey wasn't fazed as he calmly slotted past John Filan to restore parity.
Teale continued to tease Coventry on the right wing but it was Micky Adams' men who should have gone in ahead.
Benjamin volleyed against the post on the stretch before Filan produced an amazing double save.
The keeper saved low down when Michael Doyle latched onto Benjamin's flick and he reacted quickly as McSheffrey volleyed the rebound into the ground.
Stuart Giddings was stretchered off before half-time and forced another Coventry rethink and substitute Andy Whing almost put them ahead but his header from two yards was somehow kept out by Filan.
Wigan were on top in the second period but were limited to long-range efforts as Coventry looked satisfied with a point.
But in the 68th minute the visitors edged in front when Ellington produced a stunning 25-yard volley which gave Bennett absolutely no chance.
Teale could have made it 3-1 late on but blotted his copybook when he lashed over from ten yards when he was in acres of space.