After a Bournemouth corner was half-cleared, a superb Lewis Cook pass sent Stanislas through in the right channel and his low cross was flawless for Wilson to tuck away past De Gea.
United now sit second in Group H but they're five points adrift of Juventus after the Italians put-in an impressive performance to secure a 1-0 victory at Old Trafford in the reverse fixture two weeks ago with Paulo Dybala scoring the only goal of the game.
Bournemouth went close to taking the lead at the beginning of the second half, but David Brooks' impudent flick from close range was well saved by De Gea, who managed to grasp the ball at the second attempt.
He was then taken off in the 78th minute.
Tuilagi return has England dreaming again
Tuilagi was withdrawn from the bench on the eve of the stirring 12-11 victory over South Africa after sustaining the injury during training at the squad's Portugal camp.
And just when the game seemed to be heading to a stalemate, Marcus Rashford scored the victor from close range in the injury time to seal all three points for the Red Devils.
Jose Mourinho's side struggled in the early part of the first half and was duly punished by the rampant home team.
"I think by the end of December, which is the end of the first half of the Premier League, I think we are not going to be in the position we are now". Fraser drops back into a wing-back role with Stanislas supporting Wilson in the final third. We just need that consistency for the whole game. I was not at the warm-up but my assistants were telling me this is the best warm-up of our season, everybody very focused with a great intensity.
Buoyed by what Mourinho called "calm" words at the interval, United was a transformed team in the second period and several times went close to scoring.
Theresa May says will not agree Brexit deal 'at any cost'
Work is continuing on this, he said, adding: "Don't be under any illusions that there remains a significant amount of work to do". This has turned into a mess that nobody voted for and it's only going to get worse.
But the visitors were vastly improved after the break, with Herrera influential, and fellow substitute Marcus Rashford's scrappy stoppage-time strike stole the three points. Fred was also at times found ball watching and was not convincing going forward.
Chris Smalling had a hard game against Bournemouth, as the centre back looked shaky for large spells of the game.
When asked about the team's slow start, Mourinho said: "I can't understand it".
Mourinho will know, however, there must be much more to come if they are to revive their challenge for a top four place.
Ariana Grande Knew Pete Davidson Would Mention Her On ‘SNL’
Listen to Newsbeat live at 12:45 and 17:45 every weekday on BBC Radio 1 and 1Xtra - if you miss us you can listen back here. Ariana Grande has seen The First Wives Club . "His voice and laugh", Grande wrote in response.
The 21-year-old only arrived at the Vitality stadium this summer having impressed for Championship side Sheffield United, but has started ten of the Cherries' eleven league games so far this season.