Two goals in either half were enough to see off Chesterfield's chances of reaching the Checkatrade Trophy quarter finals.
Craig Mackail-Smith opened the scoring from the penalty spot, while a Jack Marriott brace and one from Issac Vassell completed Luton Town's 4-0 victory.
Luton had the first chance of the game, the first in the seventh minute after neat play down their left flank saw Jordan Cook square the ball to Craig Mackail-Smith, but the striker’s effort was easily gathered by Lloyd Allinson.
Both teams then preceded to cancel each other out, until the 22nd minute when a smart passing move down the Chesterfield right saw Jay O’Shea find space in the penalty area before he curled his effort wide of the target.
From the resulting goal kick Mackail-Smith was put through on goal, left back Laurence Maguire tried to intercept the pass but could only foul the striker. Referee Chris Breakspear pointed to the spot, and Mackail-Smith smashed the ball down the middle to give the hosts the lead.
Two minutes later it was 2-0, Mackail-Smith played a lofted a ball over the Spireites defence into the area, Marriott then held off Sam Hird before firing a low shot under Allinson and into the net.
Following the two goals the Spireites enjoyed a lot of possession but were unable to force any openings, with the Luton defence holding firm.
Mackail-Smith then came close to grabbing a brace, when he got to Jordan Cook’s cross before Hird and stabbed the ball goal wards, but he was denied by a Lloyd Allinson with his feet.
At the other end, the visitors came close to getting back into the game shortly before the break.
Firstly, Gboly Ariyibi won a free kick on the right flank. With men in the box it looked like O’Shea would cross it to them, before he instinctively tried to deceive Christian Walton in the Luton goal by curling the ball into the top right hand corner.
Unfortunately, his brilliant piece of skill wasn’t rewarded and the ball hit the top of the cross bar before going over.
Moments later Jake Beesley latched on to a defensive mix up and was through on goal, but he fired his right footed effort straight at Walton, and the hosts preserved their two goal advantage at the interval.
Early in the second half Luton extended their advantage when Marriott scored his second of the game.
He picked up the ball on the edge of the area, created space for himself before firing across Allinson into the bottom right hand corner of the net.
Caretaker boss Ritchie Humphreys introduced Kristian Dennis and Jon Nolan in an attempt to get something out of the game, but in truth it was the home side who looked the most likely to add to their tally.
And it proved so in the 86th minute when Luton substitutes Olly Lee and Vassell combined, with the latter outpacing Hird before beating Allinson with an emphatic finish.
Luton Town: Walton, O'Donnell, Smith (C), Gray (Lee), Cook, Mackail-Smith (Banton), Marriott (Vassell), Rea, Pelly-Ruddock, Senior, Musonda.
Subs not used: King (gk), Mullins, Bakinson, Cotter
Chesterfield: Allinson, O'Neil, Evatt, Hird (C), Maguire, Dimaio, Gardner (Mitchell), O'Shea, Ariyibi (Nolan), Simons (Dennis), Beesley
Subs not used: Parkin (gk), Angel, Daly, German.