Wilkinson scored the winning try and conversion in the 80th minute, and added two other conversions and three penalties for a personal contribution of 20 points in a match in which he overshadowed England rival Charlie Hodgson.
It was Hodgson who fired the first salvo in the battle of the fly-halves, when he slotted a second minute penalty to put the visitors, Sale, into a 3-0 lead.
But eight minutes later Newcastle's star, Wilkinson, hit back with a penalty of his own to even up the scores.
Hodgson hit back in the 18th minute, with another penalty to put the visitors back in the lead – 6-3.
But two minutes later Newcastle took the lead for the first time, through a Matthew Tait try – as the game came alive.
The 18-year-old England Sevens star surged through to stand-off Jos Baxendell, mesmerising the cover with a couple of sidesteps before simply shrugging off the tackle from Jason Robinson for a great try in the corner.
Wilkinson's conversion took the score up to 10-6 in favour of the home team – after 20 minutes.
However, Sale was not unnerved by this and reclaimed the lead with a two-minute blitzkrieg.
First Hodgson landed his third penalty to make it 10-9, before the ever elusive Sale and England magician Jason Robinson darted over for his team's first try.
It was end-to-end stuff and Robinson produced a magical try with a run through the Falcons pack from halfway for a score under the posts. Hodgson added the conversion to make it 16-10 after 24 minutes.
But Wilkinson hit back straight away with his second penalty, to make it 16-13.
Newcastle regained the lead towards the end of the first half, with a Jamie Noon try in the 35th minute.
It came from a scrum on the Sale line. With Sale expecting a drive, Newcastle ran it and Wilkinson put Noon in for a simple try. Wilkinson's conversion made it 20-16.
But Hodgson narrowed the gap to just one point with a 39th minute penalty – leaving the score at 20-19 at the break and the game evenly balanced.
Robinson was the next to score, when Newcastle paid dearly for giving away a daft penalty on halfway and Sale rumbling up to the line. Hodgson's inside pass sent in Robinson for a simple try. Hodgson's conversion made it 26-20 after 48 minutes.
Hodgson stretched that lead to nine points, 29-20, with a penalty in the 60th minute.
Twelve minutes later Wilkinson put his team back within striking distance, with a penalty that narrowed the gap to just six points – 29-23.
The scene was set for some Wilkinson heroics and he delivered, scoring a great try in the 80th minute of regulation play to take the score to 29-28 and the conversion to come.
It was set up when from a ruck the ball was whipped out to Wilkinson, who scythed through and scored that dramatic try in injury time.
Under the circumstances Wilkinson was never going to miss and he duly slotted it to put his team back in the lead at 30-29.
And that was also the winning score, which is something England coach Andy Robinson – not to mention the rest of the country – would cheer about very loudly.
For the Newcastle Falcons:Tries: Tait, Noon, WilkinsonCons: Wilkinson 3Pens: Wilkinson 3
For the Sale Sharks:Tries: Robinson 2Cons: Hodgson 2Pens: Hodgson 5