Morris and Hall-Johnson strike late to earn City valuable pointTWO goals in the final ten minutes at Old Trafford earned Norwich City's Under-21s a superb point as they drew 2-2 with Manchester United.
James Weir's second half brace looked to put the game beyond Jerry Gill's team but they were given hope when Carlton Morris scored a penalty on 80 minutes.
Ray Grant was then sent off after collecting his second yellow card but Reece Hall-Johnson struck in the dying minutes to secure a result that keeps City in prime position to finish in the top half of the Barclays Under-21s Premier League.
They face Wolverhampton Wanderers at New Bucks Head next Tuesday in the game that will ultimately decide their fate.
Elliott Bennett played his third game for the Development Squad since resuming from training after his serious knee injury, while scholars Michee Efete and Lewis Byrne-Hewitt were afforded starts.
United started the better of the two sides, with James Wilson and Patrick McNair missing early chances before they had a handball appeal turned down in City's box.
Wilson then had two speculative efforts from long-range before Louis Rowley failed to make the most of a chance from inside the box after excellent work from Joe Rothwell.
HALF-TIME: Manchester United 0-0 Norwich City
City will have hoped to have been more productive going forward after the half-time break but it was Andreas Pereira who had the second period's first chance.
The Manchester United midfielder tried his luck from just outside the box, and Matthews was more than equal to it.
United pressure told on 70 minutes when they got the game's first goal through substitute Weir - Rothwell's cross from the right was deflected over Matthews, leaving Weir with a simple tap-in at the far post.
Weir then notched his and his team's second six minutes later with a comfortable finish from a fluid United move, leaving City's hopes of coming with anything looking slim.
However, they were given a lifeline on 80 minutes when the referee awarded a spot-kick that Morris duly dispatched with confidence.
Grant's red card followed after a second booking, yet Gill's side still harboured hopes of getting something from the game and they got their reward in the final minute in dramatic fashion.
Morris twisted and found enough space to play in Hall-Johnson, whose deflected shot beat the 'keeper to earn the Canaries a magnificent point.
FULL-TIME: Manchester United 2-2 Norwich City
GOALS: Red Devils: James Weir (70, 76) - Canaries: Carlton Morris (pen 80), Reece Hall-Johnson (90)
MANCHESTER UNITED: J.Pereira; Varela, McNair, Ekangamene, James; Janko, Pearson, Rothwell, A.Pereira, Rowley; Wilson (Weir 62). Subs not used: Gollini, Rudge, Harrop, McConnell.
NORWICH CITY: Matthews; McNeil, McFadden (c), Awuah, Efete; E Bennett, Norman, Grant, Byrne-Hewitt (Cole 78); Hall-Johnson; Morris (Fox 90). Subs not used: Killip (GK), Ashley-Seal.