Despite an inspirational performance from the England fly-half, who was a veritable one-man show for the Falcons, the North-Easterners found themselves just edged out of the contest and ever closer to the oblivion of being relegated.
Wilkinson opened the scoring with a penalty goal in the third minute, but that advantage was soon cancelled out by his Wasps counterpart Alex King who replied in kind some three minutes later.
The sides remained level until the 24th minute, when Wasps winger John Rudd took a scoring pass and raced away for the only try of the match.
With King converting, that made it 10-3 to Wasps, but Wilkinson was able to keep his team within a point of the home side with a penalty and drop-goal.
It was desperately close in the second half too, both sides throwing everything they had into defence and scoring chances of any variety very few and far between.
Eventually, after a period of pressure from the Wasps pack, King was able to stretch his side's lead by another three points.
Wilkinson replied in kind with a penalty kick in the 72nd minute, after which the home side closed the game down very effectively to hold on for the win.
For London Wasps:Tries: RuddCons: KingPens: King 2
For Newcastle Falcons:Pens: Jonny Wilkinson 3DG: Jonny Wilkinson