Eddie Howe's side were beaten 2-0 by United at Wembley five weeks ago in their first major final for 24 years.
But Newcastle might swap silverware for a lucrative Champions League berth and second half goals from Willock and Wilson at a raucous St James' Park moved them closer to that ambition.
Newcastle's third successive league win - and their first against United since 2019 - took them above their fourth placed opponents on goal difference.
They sit one point ahead of fifth placed Tottenham, who visit Everton on Monday, as the race hots up to qualify for next season's Champions League via a top four finish.
It is 46 years since Newcastle last finished above United, but the Magpies, fuelled by Howe's astute management and the financial backing of their Saudi owners, now have a rare chance to emulate that feat.
"We were frustrated not to lead at half-time, but I felt if we performed the same way it would come. Thankfully it did," Howe said.
"If you're playing well that's the most important thing. That gives us a great chance of achieving a special season. If we can maintain our position I'll be very happy."
United are without a win in their last three league games, thrashed 7-0 at Liverpool and then held to a goalless draw by lowly Southampton before this setback on Tyneside.
United's first major trophy in six years was supposed to be the start of a new golden era, but instead they have failed to score in three successive league matches for the first time since February 2020.
It was a dispiriting start to a busy run of nine fixtures in April as Erik ten Hag's men look to nail down a top four finish, while aiming to advance to the Europa League semi-finals and FA Cup final.
"I hate to say it but they were better today, especially their determination, passion and desire. They wanted to win more so they won," Ten Hag said.
"It wasn't good enough. We allowed them too many chances. You have to be hungry and give everything every game.
"We have to deal with the setback and learn a lesson. I believe we'll bounce back."
Newcastle's pressure was finally rewarded in the 65th minute when Bruno Guimaraes clipped a cross to the far post and Allan Saint-Maximin headed back towards Willock, who nodded home from virtually on the goalline.
Wilson put the result beyond doubt after 88 minutes with a clinical close-range header from Kieran Trippier's free-kick.