The Dons took a third minute lead when Carl Regan shot home after an effort from Lloyd Dyer was blocked.
But the Dons then lost centre-back Sean O’Hanlon midway through the first half after he suffered a facial injury.
The Dons looked in little danger and continued to control the game despite losing midfielder Colin Cameron who limped off after a heavy challenge from Gary Croft.
The game looked all over when substitute Jemal Johnson smashed home a long-range shot in the 55th minute.
But Lincoln fought their way back into the game and pulled a goal back on the hour. Lee Beevers was unlucky with a header but Ben Wright forced the rebound into the net for his 13th goal of the season.