The Hatters dominated for the first 70 minutes but could not find the net and they almost paid the penalty as Lincoln came back strongly towards the end.
But the home team, who also needed the three points, now have only a faint hope of reaching the play-offs despite going on a five-match unbeaten run.
Lincoln threatened in the fourth minute when Scott Kerr broke through the middle but his final pass was inches away from Ben Wright.
But Luton were always in control and Chris Martin went close with a shot which was deflected straight at Lincoln keeper Rob Burch.
Luton lost Lewis Emanuel in the 18th minute when he went down with a knee injury and had to be stretchered off but substitute Michael Spillane slotted in well at the back and Luton always looked comfortable.
Martin caused problems for the home team in the 32nd minute when he turned defender Paul Green inside out but sent his final shot wide.
Luton had a great chance five minutes before half-time when Tom Craddock picked out Keith Keane with a cross from the right flank.
Keane found himself unmarked and six yards out but the ball stuck under his foot and trickled straight into the arms of Burch when it looked easier to score.
At the other end Lincoln went close when a header from Lee Beevers was headed out from under the bar by David Livermore.
Luton almost got the goal they wanted in the 48th minute when Lincoln failed to clear a ball into the box and George Pilkington beat Burch with his header only to see the ball come back off the bar.
Craddock shot wide and Luton pushed forward again in the 81st minute. Asa Hall set up Claude Gnakpa but, from 25 yards out, the midfielder shot wildly off target.
Lincoln sub Andy Hutchinson, brought on for his senior debut, pepped up the home attack but Luton always looked the more likely team to win it and went close again in the last minute when Craddock got clear only to see his shot saved by Burch.