The 18-year-old scored from close range either side of half-time, and Robin van Persie also found the net as United defeated Hull 3-1 in their final home game of the season.
This year may have been the worst in recent memory, but at least United ended on a high thanks to impressive performances from Wilson, fellow debutant Tom Lawrence and 18-year-old playmaker Adnan Januzaj, who was superb throughout.
But for all the energy shown by the three youngsters, it was Giggs who drew the biggest cheer of the night when he came off the bench with 20 minutes to go.
He will not be manager here next year, or may not even play a game for the club again.
Giggs, who is expected to be replaced by Louis van Gaal, wrote in his programme notes that he had not made up his mind about his future, but he added that it had been "an honour and privilege" to manage the club's final three home games of the season.
Giggs, who almost capped off a perfect night when he curled a brilliant 25-yard free kick over the wall towards goal - Eldin Jakupovic saved superbly - spoke in similar terms after the final whistle, out in the middle of the Old Trafford pitch.
"We know it's been tough this season," Giggs admitted. "Over the years we've been spoilt with the success we've had but you've always supported the team and the staff and I'm sure in the coming years we'll bring you more success.
"I'd just like to say keep supporting us, you've seen a little glimpse of the future, we always play attractive football - keep supporting us and the good times will come back soon."
The midfielder said he was in two minds as to whether he should continue playing under Van Gaal, should the Dutchman take over in the summer.
Giggs showed signs that he is still up to the job, though, as his 40-year-old legs sprinted past Alex Bruce late on.
Vidic, though, is definitely off to pastures new. "I had so many great time here," he said. "It is hard to speak because of the emotions. Most important I would like to thank the players, the manager and all the coaches. Thank you for everything and especially to the fans, you have been fantastic to me all these years."
Vidic had little to do in his farewell match. Hull were rather abject throughout. Matty Fryatt's long-range strike was the only positive for the FA Cup finalists.
The only downside for United was that Phil Jones was taken to hospital after he suffered a shoulder injury jumping for the ball with Maynor Figueroa in the first half.
Vidic was not in the starting XI, but he took centre stage just before kick-off. The Serbian received a gift, wrapped in United-coloured paper, from Sir Bobby Charlton on the touchline. Rio Ferdinand and Patrice Evra - who could also leave this summer - were not in the squad.
Wilson threatened to steal the limelight in the second minute when he shaped to shoot inside the box, but Alex Bruce came to the rescue with a diving interception.
Unlike in their first two matches under Giggs, United were flying early on. Januzaj slipped into the box after latching on to Antonio Valencia's chip, but he was hacked down by Figueroa. Referee Craig Pawson waved play on despite the protests of the home side, and then United's dominance started to fizzle out. The hosts were forced into an early change when Jones and Figueroa clashed shoulder to shoulder while in mid-flight.
Jones came off worse. He was immediately substituted, wincing with pain as he walked down the tunnel. Vidic came on to huge applause and a standing ovation.
The crowd were on their feet again on the half hour as Wilson scored the opener. The youngster volleyed home from close range after Marouane Fellaini knocked down Januzaj's free-kick at the back post.
A huge smile stretched across the striker's face as "There's only one James Wilson" rang out across the pitch from the Stretford End.
Januzaj drew a top-class save from Premier League debutant Jakupovic, and Vidic was desperate to go out with a bang. The big centre-half was a constant menace in the box when he came up for set-pieces and he thought he may have had a penalty when Stephen Quinn handled the ball in the box.
The night belonged to Wilson though. The striker was in the right place at the right time to fire United into a two-goal lead on the hour.
The ball dropped to Wilson after Jakupovic spilled Fellaini's shot and he tucked the ball home. The crowd sang "Wilson for England" as the smiling teenager celebrated.
Those celebrations were cut short a minute later when Fryatt knocked the ball past Carrick and blasted a 26-yard shot past David de Gea.
Van Persie scored late on. By then, though, Giggs had caused the biggest cheer of the night when he started warming up.
They may not see his like again.