Luke Beckett's first-half strike set Huddersfield on their way to victory over a Luton side who had Paul Furlong sent off just after the interval.
Beckett put the Terriers ahead when he planted a shot past two defenders on the line after 36 minutes.
Luton, who earlier went close through a Paul McVeigh header, then had Furlong sent off for a second caution.
And Danny Cadamarteri raced on to Andy Holdsworth's through-ball to seal the win with 30 minutes remaining.
Huddersfield: Glennon, Sinclair, Nathan Clarke, Keogh, Skarz, Kamara, Wallwork, Holdsworth, Brandon (Young 80), Beckett (Booth 86), Cadamarteri (Collins 72).
Subs Not Used: Smithies, Mirfin.
Booked: Nathan Clarke, Holdsworth, Keogh.
Goals: Beckett 36, Cadamarteri 60.
Luton: Alnwick, Jackson (Andrew 68), Perry, Fojut, Goodall, Bell, Robinson, Spring, Morgan (Currie 46), McVeigh (Talbot 46), Furlong.
Subs Not Used: Coyne, Edwards.
Sent Off: Furlong (47).
Booked: Bell, Furlong, Andrew.
Ref: Dean Whitestone (Northamptonshire).