Three goals in five second-half minutes helped Luton secure victory over struggling Alfreton.
Paul Clayton spurned a great opportunity to put the visitors ahead when he raced through on goal, but his effort was saved by Mark Tyler.
And they were made to pay with JJ O'Donnell's close-range finish, before Jonathan Smith's header made it 2-0.
Andre Gray then made the points safe when he smashed home after good work from Ronnie Henry.
VIEWS FROM THE TRAINING GROUND
Luton manager Paul Buckle told BBC Three Counties Radio:
"We were poor on the day up there [when Luton lost 3-0 at Alfreton in September], we were awful, but a lot's happened since then.
"We've recovered really well and we've marched on in the league, we've marched on in the cups, and the boys are on a good unbeaten run at the moment.
"The players are not in any mood at the moment to give up what they've built - and it's been built on work-rate and desire. In these winter months now, I really feel we're upping our game.
"We're looking forward to it, we know it's going to be a tough game because they're a good side, but there again that's nothing new."