Goals from Adam Newton, Alan White and Claude Gnakpa eased the classy Hatters past the League Two high-flyers in a surprisingly one-side game.
Rossi Jarvis cleared Rotherham skipper Ian Sharps’ shot off the line before Newton put Luton ahead in the seventh minute when he collected Kevin Nicholls’ low cross and coolly dummied goalkeeper Andy Warrington before slotting the ball into the empty net.
The Hatters piled forward and White doubled their lead in the 19th minute with a towering header from skipper Nicholls’ free-kick.
Luton continued to dominate after the break with some slick passing football and it came as no surprise when Gnakpa made it 3-0 in the 68th minute.
The Frenchman cut inside from the left flank and blasted a right-foot rocket into the bottom corner from 22 yards, before Millers substitute Drewe Broughton headed against the bar nine minutes from the end.
Luton will travel to Southampton in round three on January 2.