Everton got off to a bright start, but United got the game’s first real chance when Bruno Fernandes flashed the effort wide.
The chance led to a scuffle between Idrissa Gueye and Michael Keane, and the former was sent off for shoving the latter.
Despite the numerical advantage, United could not take control of proceedings, allowing Everton to grow in confidence.
Kiernan Dewsbury-Hall drew the first blood with a superb strike, bending the ball into the bottom corner and beyond the reach of goalkeeper Senne Lammens.
United almost got an immediate response when Amad fired a shot straight at Jordan Pickford.
Pickford made a superb stop to deny Bruno Fernandes from restoring parity for the hosts before the break.
Manager Ruben Amorim made one change at the interval, replacing Noussair Mazraoui with Mason Mount.
The substitute and Casemiro flashed their efforts wide as United cranked up the pressure early on in the second half.
Pickford pulled off a brilliant stop to deny Bryan Mbeumo, and Mount curled a shot wife just immediately after the Cameroonian’s effort.
Fernandes squandered a big opening after Mount’s brilliant work, missing the target from eight yards out.
Pickford came up with another big stop, this time keeping out Joshua Zirkzee’s header from finding the back of the net.
Just before the stroke of full time, the Everton goalkeeper did superbly yet again, tipping the Dutchman’s header over the bar.
The result marked the Toffees’ first league win at Manchester United since 2013.