The Millers chances on the night were blown and the tie was effectively over in the first 20 minutes as the Hatters took a two goal lead.
Despite the visitors making the better start, with Ian Sharps' header cleared off the line, it was Adam Newton that gave the home side the lead, sidefooting home on seven minutes after neat approach play by Kevin Nicholls.
The lead was then doubled on 19 minutes as veteran Alan Whyte thundered a header past Andy Warrington from Nicholls' free kick after Steve Brogan had bodychecked Claude Gnapka.
Gnapka, a threat in the first game 10 days ago, was heavily involved in Luton's good play and crossed for Kevin Gallen just before the break, but his header whistled over the crossbar.
Fortunes didn't improve after the break for the Millers despite Adam Le Fondre's effort straight at 'keeper Kevin Pilkington.
And Gnapka put an end to proceedings on 68 minutes as he fired past Warrington from just outside the area.
Brogan then struck a free kick just over before a double substitution saw Taylor and Broughton replace Pope and Ellison.
Broughton came the closest to netting a consolation but his header from five yards bounced off the bar with four minutes left before Luton finished strongly in the dying seconds, booking their trip to St Mary's with ease.