Zlatan Ibrahimovic sparked United into life with a superb opener before Sebastian Larsson was sent off for a risky tackle, leaving space for Henrikh Mkhitaryan and substitute Marcus Rashford to seal the three points after the break.
"I feel like Benjamin Button - I was born old and I will die young".
Meanwhile, Romelu Lukaku's double ensured Craig Shakespeare's flawless record as Leicester manager was ended at Goodison Park.
Bailly is one of six United players aged 24 or younger that have 10 or more league appearances this season with several other youngsters in the squad yet to play.
The result moves Jose Mourinho's side up to fifth in the table, 3 points above sixth placed Arsenal, who play Crystal Palace on Monday. A large part of the reason they're that short is the quality of opposition left in the competition.
Ibrahimovic opened the scoring in the 30th minute, swiveling brilliantly and firing home from outside the box.
Before the referee blew the whistle for half-time, the Black Cats were reduced to 10-men when Seb Larsson was given questionable red card for his challenge on Ander Herrera.
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Re Virgin, the RMT said it has been seeking an "explicit clarification" from the company on the retention of the role of the guard.
Rashford capped a comfortable win in the 89th minute when United broke and Ibrahimovic teed up the England youngster to fire a fizzing shot into the bottom-left corner from an acute angle. "That is felt with a team close to relegation".
"But we played very well to win 3-0". We controlled the game well. "The Premier League was not possible because we drew too many matches".
"He played really well, so good hour for him".
Manchester United sit four points back of fourth place Manchester City with a match in hand.
Asked about the Luke Shaw situation which has seen the defender publicly criticised by manager Jose Mourinho he said: "He has been doing good". In his new position he can create more.
But after defeating the basement side, the Portuguese told Sky Sports: "I told him it was a very solid performance". I'd love to play in the games coming up and especially with the Europa League to help the team push towards the final.