Just short of 100 unhappy Vale fans staged a protest outside the ground before kick-off, calling for the removal of manager Dean Glover and for the club to be put up for sale.
And they soon had more ammunition to vent their frustrations as Luton controlled much of the early play.
The visitors were inches from taking an 18th-minute lead when Chris Martin's 20-yard shot was deflected against Joe Anyon's left-hand post.
Ian Henderson's follow-up shot was then blocked close to goal to ignite the first murmurs of dissent from the Vale faithful.
But Vale were given a huge boost when they took the lead with their first effort on goal in the 25th minute.
Mark Bower was booked for a foul on Kevin Gall at the right edge of the penalty area and Adnan Ahmed's free-kick was clipped home by John McCombe's right foot from eight yards.
Vale should have doubled their lead shortly afterwards when Dean Brill made an excellent double save to deny Gall, who ran clear from Scott Brown's pass.
And Luton made them pay two minutes before the interval with a deserved equaliser by Asa Hall, who fired his eighth goal of the season.
Vale were caught short of numbers at the back and Hall had time to pick his spot from Henderson's pass, slotting the ball inside Anyon's left-hand post from 14 yards.
The visitors took the lead seven minutes into the second period, with Kevin Gallen side-footing past Anyon from point-blank range after Tom Craddock had skinned Luke Prosser.
Vale rallied briefly with Brill saving well from Brown and McCombe's header from Ahmed's resulting corner cleared off the line by Sol Davis.
But it was as good as over in the 63rd minute when Martin beat Anthony Griffith to a long pass from Hall and belted a low shot which struck Anyon before rolling in.