Nineteen-year-old Dave Hibbert was handed his first start of the season and he repaid his manager's confidence with two magnificent goals.
Lee Matthews rubbed salt in Luton's wounds nine minutes from time, pouncing on his own rebounded penalty to slot home for Vale's third.
The travelling side showed why they are top of the league after just six minutes of action.
Kevin Foley bagged his second goal of the season when he got on the end of a perfectly weighted pass from Rowan Vine. Vine's throughball split Vale's back four and Foley calmly slotted the ball under the advancing Mark Goodlad.
The visitors could have had their second just seven minutes later. A flowing move involving seven players opened up space for left-back Sol Davis to whip in a cross, but Luton danger man Ahmet Brkovic, being harassed by Michael Walsh, steered his shot wide.
With their backs against the wall for much of the first half, Vale managed to snatch an equaliser before the half-time whistle. Michael Cummins' sweet first-time ball gave Hibbert a sight on goal for the first time of the game and he made no mistake, firing the ball past keeper Marlon Beresford.
After a workmanlike first-half display, Vale came out all guns blazing after the break.
They should have been ahead after nine minutes of second half action when Luton could not deal with a Chris Birchall corner and, when Danny Sonner misjudged his long range effort, the danger looked like it had passed. However the ball sat up nicely for Jeff Smith to strike through a wall of Luton defenders and off the post.
Encouraged by the chance and Luton's defensive frailties, the home side continued to apply the pressure and they got their reward in the 59th minute.
Cummins jinked his way into the box, and Luton's attempted clearance fell to the feet of Hibbert, who grabbed his second of the game and season with a delightful right foot chip into the top corner of the net.
Vale secured the points with a third late in the game when Billy Paynter was brought down in the Hatters penalty area by Curtis Davies and Matthews tucked away the rebound after his spot-kick came back off the upright.