Wolves were leading through Bakary Sako's 51st minute strike before Dicko kept Wolves firmly on course for an instant return to the Championship with his quickfire double - that should have become a hat-trick only for him to miss a last minute penalty.
Dicko then ended Vale's comeback hopes with his brace as Micky Adams' side crashed to a third successive defeat.
Dicko bundled home his first from close range in the 73rd minute after a cross from skipper Sam Ricketts and then used his power to hold off the challenge of Carl Dickinson and beat Neal with an unstoppable drive.
Things could have been very different had Vale taken the one clear chance to come their way when the game was goalless.
They should really have broken the deadlock in the 25th minute and paid the price for a poor piece of finishing from Tom Pope.
After Wolves midfielder Jack Price had given the ball away, Billy Knott released 13-goal Pope who only had goalkeeper Carl Ikeme to beat but Pope wastefully lifted the ball over the bar from 12 yards.
It was a major let off for Wolves who were then frustrated themselves seven minutes before half time when Ricketts headed a James Henry cross against the bar before Sako and Dicko finally made some persistent pressure pay off.
Dicko then had the chance to help himself to the match ball after Chris Lines had fouled Henry only to see his spot-kick saved by Neal.
- Sports & Recreation
- Bakary Sako
- Chris Neal
- Sam Ricketts
- Jack Grimmer