The visitors, who started the game with a trio of first team players in Leon Osman, Steven Pienaar and Arouna Kone, rarely troubled United stopper Anders Lindegaard in a game which took almost 80 minutes to come to life.
Both teams started conservatively, and the hosts came closest to breaking the deadlock through Nick Powell, but he could only watch as his goal bound header was cleared off the line.
And Everton had to rely on the brilliant Jonjoe Kenny and goalkeeper Russell Griffiths to keep the score 0-0.
Considering a place at the top of the league was at stake, the opening 45 minutes was an underwhelming affair.
Everton started off with much of the possession but they weren’t able to do a great deal with it as the first few minutes went by without an effort.
Ironically, it was Manchester United who had the game’s first shot as Powell’s low strike was palmed away by Griffiths, before the striker went close from a corner seconds later.
It took a little while longer for Everton to join the party when Osman found Kone alone at the back post, but United defender Reece James was able to throw himself in the way of the ball to block the Ivorian’s volley.
The closest either side came to breaking the deadlock in the first half was again through Powell, but his header was cleared excellently off the line by Ryan Ledson, keeping the scores level.
The first real effort of the second half fell to United under-21s’ joint- top scorer James Wilson, but Griffiths was equal to it.
And the longer the game went on, the more the hosts looked like nicking it as sustained pressure saw Griffiths put into action yet again, but he did well to keep out Andres Pereira’s shot at full stretch.
Pereira went close once more, but he was unfortunate to see his curling effort from outside the area whistle past the post.
There was, however, some late drama as Lindegaard fell into his own goal with the ball at the death after a routine catch from a free kick. But he was adjudged to have been impeded by Brendan Galloway and The Toffees were denied a late winner.
Manchester United U21: Lindegaard (GK), da Silva (Willock, 61’), Thorpe, Blackett, James, Grimshaw, Love, Weir, Wilson, A Pereira, Powell (Harrop, 41’) Subs: J Pereira (GK), Harrop, Willock, Fletcher, Kellett
Booked: da Silva (60’)
Everton U21: Griffiths (GK), Jones, Connolly, Ledson, Kenny, Galloway, Henen, Osman, Kone (Charlsley), Dowell, Pienaar Subs: Hunt (GK), Charsley, Green, Walsh, Langton,
Booked: Kenny (53’)
Referee: Anthony Tankard (Yorks)