Jordan Rhodes scored a dramatic late winner to send Huddersfield to within 90 minutes of an unlikely Premier League return.
The much-travelled striker, who replaced the injured Danny Ward during the first half, struck in predatory fashion with just eight minutes remaining.
Sorba Thomas delivered a deep free-kick to the far post where Rhodes showed desire and a predatory instinct to divert the ball into the net.
Huddersfield fans roared their delight as Carlos Corberan's team booked their place in the Championship play-off final.
They will face Nottingham Forest or Sheffield United at Wembley on May 29 for a place in the Premier League, where they spent two seasons after winning promotion under David Wagner five years ago.
After finishing a dismal 20th in the Championship last term, the Terriers have been a side transformed this season.
Their high-energy approach ultimately did for Luton, who themselves have breathed much passion and romance into English football this term.
Nathan Jones' men, who operate with one of the smallest budgets in the Championship, largely dominated the first half.
Yet they could not make their chances pay and Huddersfield improved markedly after the restart.
Harry Toffolo, Town's free-scoring left-back, had gone close during the first half with a shot saved by Matt Ingram, who appeared to then haul him down in the final quarter.
Huddersfield screamed for a penalty but referee Peter Bankes was unmoved.
Nevertheless, the hosts were not to be denied as Rhodes struck in clinical fashion to spark a mass pitch invasion.
