The 22-year-old, who joined Walsall on-loan from Barnsley, fired the Saddlers ahead in the 26th minute before Dean Keates grabbed their second on the stroke of half-time.
But the intervention of Wright left County's players and fans fuming as they were in no doubt the former Leicester City marksman should have been sent-off 60 seconds before he struck.
Wright had already been booked for a foul on County goalkeeper Kevin Pilkington before crashing into him for a second time. But, rather than book him again and send him off, referee Neil Swarbrick dispensed a stern lecture and Wright took full advantage to leave County seething.
Walsall have now won nine of their 10 home league games this season - drawing the other. But, to say they were lucky to keep that record intact was an understatement.
County, who slipped to just their fourth defeat of the season, should have been in control before Wright struck only to be undone by goalkeeper Clayton Ince and a slice of misfortune.
Ironically, it was Ince who then handed County a route back into the game when he let Ian Ross's 72nd minute free-kick slip through his fingers - the first league goal Walsall have conceded at Bescot this term in 882 minutes of league action.
But Ross's first goal of the season proved to be no more than a consolation for County who were left to rue not taking their early chances.
Ince pulled off a world class save in the 17th minute to push away a fierce volley from Mike Edwards. Six minutes later Jay Smith's shot was goal bound only to be deflected wide by his team-mate, Andy Parkinson.
Walsall took full advantage of that double let-off when Mark Kinsella powered into the County area and fed Wright who drilled his drive past Pilkington.
While County were out of luck, Walsall's was in when Keates' 30 yard free-kick somehow found its way through a crowded goalmouth and passed the bemused Pilkington to effectively seal the fate of the Meadow Lane outfit.