Lewis Neal fired Preston ahead before Luton boss Mike Newell was sent off for protesting at Steve Howard's booking.
David Nugent nodded a second but Ahmet Brkovic's shot deflected in off Tyrone Mears to give Luton hope before Mears scored Preston's third soon after.
Chris Sedgwick made it 4-1 from the spot when Luton keeper Marlon Beresford saw red for fouling Mears and Claude Davis added a fifth from close range.
Luton manager Mike Newell on fourth official Steven Cummins:
"I don't want to get myself into more trouble than I'm already in, but I don't see the point in fourth officials because all they ever cause is trouble. "No-one (managers) ever gets sent off if there's no fourth official. I can't handle arrogance or incompetence from anybody.
"I can't handle it, that's why I lost my temper. I can spot incompetence and arrogance very early.
"The fourth official is incompetent and he can't do his job."
Preston: Nash, Mears, Mawene, Lucketti, Hill, Sedgwick, McKenna (Davis 66), O'Neil, Lewis Neal (Whaley 72), Nugent (Agyemang 81), Ormerod.
Subs Not Used: Dichio, Stock.
Booked: Hill, Whaley.
Goals: Lewis Neal 20, Nugent 53, Mears 84, Sedgwick 90 pen, Davis 90.
Luton: Beresford, Foley, Coyne (Barnett 41), Heikkinen, Keane (Davis 71), Edwards, Nicholls, Bell (Morgan 59), Brkovic, Vine, Howard.
Subs Not Used: Brill, Showunmi.
Sent Off: Beresford (89).
Booked: Howard, Vine.
Goals: Mears 82 og.
Att: 15,237.
Ref: D Drysdale (Lincolnshire).