Two goals in three first-half minutes from Chris Martin and a second-half header from man-of-the-match Ian Roper were enough to give the Hatters the win.
The Imps had given themselves hope with a 38th minute strike by Lenell John-Lewis and also netted through substitute Adrian Patulea in the 90th minute.
But the final result saw Luton extend their unbeaten run to seven matches as they moved to minus one point at the foot of the table.
A quiet opening period saw Martin fire into the side netting from 12 yards in the 11th minute after a Rossi Jarvis corner had been half cleared before Dany N'Guessan jinked into the area at the opposite end a minute later and saw his cross-shot deflected wide for a corner.
Janos Kovacs put a clear header wide from 10 yards after Aaron Brown's 16th minute corner and N'Guessan then robbed Keith Keane and hit an angled 15 yard drive into the arms of Conrad Logan.
The hosts responded with a slick move in the 19th minute when Kevin Gallen and Jarvis combined to set up Drew Talbot, whose left foot shot from 16 yards was tipped over the bar by Rob Burch.
John-Lewis and N'Guessan fired shots wide for the visitors before Luton took the lead in the 31st minute when Gallen helped the ball out to the right and full-back Michael Spillane's inch-perfect cross allowed Martin to power home a diving header from 15 yards.
Two minutes later the lead was doubled almost out of the blue as Martin found the bottom corner of the net with an instant 20-yard strike from Craddock's pass.
The Hatters seemed to be in command but Lincoln struck back in the 38th minute when the lively N'Guessan crossed from the left and John-Lewis had all the time in the world to find the net at the second attempt from eight yards after his first shot had hit the legs of Logan.
Luton ended the half on the offensive as Martin had a low 20-yard shot saved by Burch in the 43rd minute before Brown came perilously close to scoring an own goal in injury time, slicing the ball across his own goalmouth and wide only for referee Steven Cook to bizarrely award a goal kick.
The hosts kept up the pressure after the break with Talbot ending a 30 yard run with a 20-yard shot just wide in the 48th minute.
Two minutes later it was 3-1 as Spillane retrieved Jarvis' over-hit corner and produced great skill to deliver the ball left-footed from the left for Roper to nod home from three yards.
Jarvis then forced Burch into a fingertip save in the 54th minute with a curling 25 yard free-kick.
Lincoln made a double substitution with Patulea replacing John-Lewis and Stefan Oakes coming on for Lee Frecklington.
The changes helped the visitors and they almost pulled a goal back in the 73rd minute when Kovacs hit a 14-yard shot from the right-hand side of the penalty area that came back off the inside of the post before Logan saved Sam Mullarkey's follow up.
Patulea did find the net in the 90th minute with a left-foot finish from an acute angle after Brown's flick-on, but Luton survived five minutes of injury time to secure the win.