Wilkinson kicked one conversion and five penalties to help guide his side home but it was a late try from Hugh Vyvyan that snatched the victory from the hands of Northampton, who had scored three tries of their own in an exciting encounter – two of them from scrum-half Matt Dawson.
With second rower Matt Lord scoring his side's third try in the second half it seemed as if the game was slipping from the Falcons' grip.
But Newcastle seemed to gather their strength for one last effort, with the result that Vyvyan's try in the 79th minute put them within reach of an unlikely victory, before Wilkinson kept his nerve to add the conversion and the Falcons breathed a huge sigh of relief.
The win means that the Falcons are off the bottom of the Zurich Premiership table and with Bristol and London Irish now below them, Rob Andrew's team have every reason to look forward to the future with no little optimism.
"I always thought we were capable of causing them problems. It was just a case of plugging away and our desire to keep playing the game saw us score a great try," said Andrew in the post-match press conference.
"The courage of the side to refuse to lie down got us through the match. The way we played is a sign of a group of players which is working very hard for each other."
For Newcastle Falcons:Try: VyvyanCon: WilkinsonPens: Wilkinson 5
For Northampton Saints:Tries: Dawson 2, LordCon: GraysonPen: Grayson