Sancho netted with a clinical finish in the first half to seal United's third successive Premier League victory.
It was a well-timed contribution from Sancho, coming just hours after United officially confirmed their £82 million ($94 million) swoop for Ajax's Antony.
United manager Erik ten Hag worked with Antony in Amsterdam and the 22-year-old looks likely to be a regular in the right wing role currently occupied by Sancho.
If there are doubts in his mind about retaining his place, Sancho did his best to remind Ten Hag of his qualities with his second goal of the season.
United moved up to fifth place and sit just one point adrift of the top four as Ten Hag begins to make an impact after a nightmare start to his reign.
Beaten by Brighton and Brentford in their first two matches of the Ten Hag era, United have climbed off the bottom of the table without ever looking completely convincing.
But Ten Hag will be satisfied with his team's latest display of spirit and determination, the qualities he demanded they show after losing 4-0 at Brentford.
United were unchanged from the side that won 1-0 at Southampton last weekend, meaning Cristiano Ronaldo started on the bench for a third successive game.
Ronaldo had hoped to leave United before the transfer window shut on Thursday, but the Portugal star was unable to find a suitor willing to meet the club's asking price and his desire to play in the Champions League.
Ten Hag says he is "on the same page" with the 37-year-old striker about his role, but Antony's arrival could further limit Ronaldo's playing time.
The Brazilian did not sign in time to feature against the Foxes, leaving Sancho, Marcus Rashford and Anthony Elanga to form United's attacking trio.