Rashford somehow headed over from barely two yards out within the first five minutes, but he soon made amends, controlling Pogba's lofted pass expertly and drilling beyond Kasper Schmeichel.
However, as is often the case on the road, United relied on goalkeeper David de Gea for all three points as a Leicester side that have often troubled the top six this season improved after half-time.
But the caretaker manager, who has gone unbeaten since taking over from Jose Mourinho, carried on with the feel-good factor at United by letting players stay at home instead of braving the snow for gym work.
What does it mean?
Sanchez made the heavily publicised move from Arsenal to Manchester United last January, as United fans wait for someone to finally become a worthy successor to Cristiano Ronaldo in the prestigious number 7 shirt.
Having beaten Manchester City and Chelsea in December, Leicester earned a surprise draw at Anfield on Tuesday night to put a small dent in Liverpool's title charge, but could not mount a fightback against Marcus Rashford's early goal this time.
The youngster's goal turned out to be the eventual match-winner and Pogba played a huge part in ensuring it, controlling the game in the end when United needed him the most.
At the end of the day, Leicester have now picked up just one point in their previous four league matches.
- Only Ryan Giggs (21y 74d) has reached 100 Premier League appearances for Manchester United at a younger age than Marcus Rashford (21y 95d).
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