After a goalless first forty-five, the Hatters scored twice after the break to secure a clash with Shrewsbury Town in the final.
The hosts had the better chances in a scrappy first half. Freddie Hinds dragged a shot wide while Jack Snelus skewed a shot over shortly afterwards.
Town’s best efforts fell to Jordan Young who curled wide from 20 yards and Callum Gunner, who got up well at a corner but could only direct his header off target.
Kavan Cotter and Cameron McJannet’s radar was also slightly off when chances fell to them and Jordan Simpson - son of former Town player, Fitzroy – saw a shot from distance bounce into the arms of Luton ‘keeper, Liam Gooch before the half was over.
Hinds went close at the start of the second period, lifting a shot that landed just wide of the upright before Connor Johns got down brilliantly to turn away an effort that was bound for the bottom corner.
Midway through the second half however, the hosts took the lead. Having threatened earlier in the half, Hinds was played in on goal, streaked clear of the defence and lifted the ball over the advancing Johns into the net.
Johns was called into action shortly afterwards, beating away a shot from George Murray after the hosts had carved out a shooting opportunity for the youngster.
With Town pushing for an equaliser, the hosts sealed their place in the final in stoppage time.
Substitute James Verney was played in on goal on the left edge of the box, took the ball around Johns and slotted into the empty net.