The young guns currently sit third from bottom in the Premier League 2 table, but are unbeaten in their last five games in all competitions.
The Red Devils started slowly as Everton knocked on the door early on by forcing Keiran O'Hara into making two quick saves inside the opening four minutes.
Bassala Sambou came close to putting the Toffees in front when he launched a thumping strike towards goal, but the striker ended up dragging his shot wide.
At the other end, Ethan Hamilton got on the end of a free kick that was lofted into the box and his attempt at goal was blocked for a corner, which came to nothing.
Tosin Kehinde was inches away from being awarded a penalty when he was pulled down just outside of the box, but the intent from the midfielder demonstrated United's improvement in the second half.
As the clocked ticked down, Callum Gribbin took a chance with a left-footed strike, which was kept out of the net by the Everton shot-stopper.
In the end, though, it was Everton, who sit inside the top four, piling on pressure in the closing stages of the contest.