The visitors could have won it when Kemar Roofe fired against the bar and then saw a header well saved by Wigan goalkeeper Matt Gilks.
The campaign ended in disappointment for both sides, with Leeds missing the play-offs and Wigan finishing nine points adrift of safety.
Chris Wood made no mistake from the spot to draw his side levelReuters
Leeds made the brighter start in the Lancashire sunshine, with Roofe seeing a shot deflected just wide with only two minutes gone.
Moments later, O’Kane played in an intelligent ball to Pablo Hernandez, who fired wastefully wide from 15 yards.
But the visitors were rocked when Wigan took the lead with their first attack on six minutes.
It was the striker’s 27th league goal of the seasonReuters
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Michael Jacobs played a lovely ball through to Tunnicliffe, who showed great composure to round Green before steadying himself and slotting home from close range.
Leeds were claiming a penalty on the 15-minute mark when Wood went down under the challenge of Jamie Hanson, although the referee waved play on.
Omar Bogle, having been restored to Wigan's starting line-up, fired over from the edge of the box, before Wood warmed the hands of Gilks at the other end.
After a relatively quiet first half, the game burst into life just after the restart.
The visitors were awarded a spot-kick just four minutes into the second period, when O'Kane took a tumble inside the Wigan box.
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