The former Sheffield Wednesday hitman netted a 43rd minute penalty and then added a second in the 75th minute to make sure the Hatters came out on top against the Chairboys.
It looked as though Jermaine Easter might come back to haunt his old club after he gave Wanderers a 34th minute lead.
But Jim Gannon's men hit back in fighting fashion to deservedly book their place in the next round.
Wycombe started well and in the ninth minute Matt Bloomfield saw his powerful 25-yard drive tipped over the bar by Stockport keeper James Spencer.
A minute later Stefan Oakes went agonisingly close with a left-foot shot but his effort flew over the bar from a tight angle.
At the other end Proudlock attempted an ambitious chip from the edge of the box but it didn't trouble Young.
Tes Bramble whipped a cross from the byline as County opened up Wanderers, but Proudlock was a second too late to guide the ball past Young for the opener.
Wolves' loan midfielder Stephen Gleeson produced a wonderful piece of individual skill to dance past two defenders but his side-footed shot was well-saved by Young.
County were made to pay for their misses when, in the 34th minute, Easter put his former club behind.
A good cross from Kevin Betsy found the striker unmarked at the back post. He wasn't going to miss from close range and headed past Spencer for his first cup goal of the season.
Bloomfield fired wide a minute later as the visitors had a glorious chance to double their advantage.
But then County should have levelled. A superb pass from Gleeson found Proudlock but, with the only the keeper to beat, the striker allowed Young to save low down.
However, the home side got their rewards for some sustained pressure. Former Manchester United youngster David Poole was felled in the Wanderers penalty area and Proudlock made no mistake from the spot.
Wanderers went close to regaining the lead four minutes after the resumption. Oakes fired over from distance before just after the hour mark Betsy fired over the bar with a left-foot shot.
County came close to scoring themselves in the 65th minute. Keith Briggs slid in at the back post as Wanderers failed to deal with a corner, but the midfielder was unable to get the slightest of touches needed to direct the ball past Young.
But the home side's second goal did come eventually. Poole burst free on the right wing, squared the ball to Gleeson who in turn squared for Proudlock to fire home from just inside the area.