كتب : Amro Hassan
Relegations strugglers Sion are now eighth in the Swiss Super League table with 33 points, awaiting the result of ninth-placed Lucerne against Grasshopper on Sunday.
French midfielder Virgile Reset scored the only goal of the game on seventh minute.
Al-Hadari, who was starting his fourth successive game after a period where he lost his regular spot, produced a number of important saves to hand Sion all three points.
The former Ahli man did well to keep Neuchatel at bay in the fourth minute, before catching another cross right before it reached the visitors' striker 15 minutes from time.
In injury time, the 35-year-old once again made a heroic save to deny a Neuchatel player who was clear on goal.
The win will be a confident booster for Sion, who will meet Young Boys in the Swiss Cup final on Wednesday.