The defeat left the Cheshire side closer to the drop as Brighton snatched a late point against West Ham.
Crewe stay out of the bottom three on goal difference, but with a trip to promotion-chasing Ipswich lying in wait next weekend, their final match of the season at home against Coventry is almost certain to be a must win affair for Dario Gradi's troubled outfit.
Relegation has crept up on them as, after reaching the heights of eighth after a 2-0 win at Leeds, they have not won a game since.
The sale of Dean Ashton to Norwich has hit them hard and Gradi's men just lack the quality in the penalty box to turn the sort of chances they created against Stoke into goals.
Three times in the first half they missed good openings. First Andy White dragged an effort past the post and then Mark Rivers sliced a first-time shot from the edge of the box well wide after a neat three-man move.
White also had a goal chalked off from a corner after he bundled Stoke keeper Steve Simonsen into the net.
Anther flagkick saw Colin Murdock's downward header rise off the turf towards the top corner only to be deflected clear by Neal.
Although Crewe had the better chances, Stoke were always on top in a poor quality game in which Noel-Williams was the pick of the strikers on display.
The former Watford man missed a sitter in the 72nd minute when Michael Ricketts found him with a far post cross, but he failed to connect cleanly with his head with the goal at his mercy and the ball went wide.
The derby reached a turning point in the 75th minute when David Vaughan dragged a good chance past the far post with just Simonsen to beat.
Four minutes later, Noel-Williams pumped a deep cross to the back stick were Chris Greenacre headed back across goal for Neal to finish with his head.
Crewe were sunk two minutes from time when Neal passed the ball into Noel-Williams' feet and the striker turned on the edge of the six-yard box past Richard Walker and fired home.