The England striker put the Magpies ahead in the 16th minute of their quarter final, guiding in a wonderful finish with the outside of his boot.
However, his run from the halfway line at Stamford Bridge was only made possible due to some appalling defending from the home side.
First, Moises Caicedo seemed to give up on tracking back, and then Thiago Silva's attempted tackle bounced off Wilson and straight forwards.
That disruption allowed Benoit Badiashile to get in between Wilson and the ball, seemingly ending any danger, but then the French defender somehow stumbled over and left the ball to Wilson to finish.
Chelsea fans haven't had much fun watching their team this season, and a number of fans behind the goal took their frustrations out on Wilson.
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The 31-year-old wasn't having any of it though, and directed a shush at the fuming fans and he celebrated directly in front of them.
Speaking on talkSPORT, England legend Stuart Pearce commented on a later error, saying: "Badiashile, I'm not sure what you're trying to achieve.
"Honestly, he's just so loose, he's cost his team a goal already and now he's ended up passing the ball across the face of the 18-yard box and he's given it away.
"Badisashile has been a disaster in the first half."