City never looked back after taking the lead on six minutes when Lee Beevers ran unchallenged at the Crewe defence before finishing from 20 yards.
Beevers almost added a second goal on 31 minutes when his far-post header brought a fingertip save from Crewe keeper Ben Williams.
Crewe went further behind after 35 minutes. Midfielder Kenny Lunt was yellow carded for fouling Derek Asamoah just outside the box and the Crewe defence only half cleared the free-kick.
Gary Birch put the ball back into the box and Maheta Molango finished with a first-time shot.
Crewe rarely threatened but pulled a goal back a minute before the break.
David Vaughan sent a free-kick into the box which was headed home by centre-back Richard Walker.
Crewe were forced to substitute goalkeeper Williams at half time after he suffered a calf injury and his replacement Stuart Tomlinson fared little better.
Lincoln restored their two-goal lead in the 64th minute when midfielder Nat Brown saw a header come back off the post which was turned in by Birch.
Three minutes later Birch brought his tally for the season to five when he turned inside the box and shot home off the post.
Crewe's night of misery was completed eight minutes from time. Lincoln's summer signing Scott Kerr tore the defence apart down the right before firing over a perfect cross and Marvin Robinson, who had only been on the pitch for two minutes, scored with a superb glancing header.
Crewe's strikeforce in the second half posed virtually no danger to the Lincoln defence.
New signing Juan Ugarte, given his full debut, failed to muster a single shot on target and was pulled off half an hour from the end.