REPORT: Lincoln City 1 Wigan Athletic 3
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Latics were off to the perfect start when Josh Magennis nodded down Max Power's floated delivery into the path of Lang, who volleyed home from close range with only eight minutes gone.
However, Lincoln were level within six minutes when a deflected shot found its way to Anthony Scully, who took his time before slotting past Ben Amos.
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Hide AdCredit Latics, though, they regained their composure and went back in front midway through the first half, when Will Keane bagged his 22nd goal of the campaign.
Keane then squandered a fantastic chance to make it 3-1 when, after Power had played him in, he fired straight at the goalkeeper.
The rebound looked as though it would be tapped home by Lang, only for a defender to bundle it round the post from almost on the line.
Latics needed a fine save from Amos to keep them in front at the break.
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Hide AdBut they continued their dominance in the second period, with Kell Watts firing just wide from 15 yards, before Keane somehow did likewise after being picked out by Lang.
Magennis was denied by a fantastic save, before Lang made it 3-1 with 18 minutes to go, with a brilliant finish into the bottom corner of the net.
To cap a perfect day, second-placed MK Dons were held 1-1 at relegation-threatened Wimbledon and third-placed Rotherham were beaten 1-0 at home by struggling Charlton.
Latics are now three points clear of MK and six ahead of Rotherham, with two games in hand on the former.