The game was goalless until the 83rd minute when Andrew Johnson curled home the opener from a free kick. However, Celtic grabbed an equaliser on 86 minutes when Raul Correia lobbed Dan Lowson.
The visitors started the game well but it was their custodian Liam Hughes who was forced into the first save as he denied Andrew Johnson from a corner on 9 minutes.
Morpeth tried to seize the initiative in the game as Sam Hodgson fashioned two opportunities in a minute; the first he drove the ball a few yards over the bar and the second he was picked out in space but his downwards header lacked the power and it was comfortable for Hughes.
The visitors showed that they were not content to sit back and soak up pressure and came roaring back themselves; Connor O’Grady forced Lowson into a smart save on 13 minutes as he ‘keeper was called to tip a header away.
A minute later, Justin Johnson was put clear on goal but the young striker was only able to shoot straight at Lowson who could make the comfortable save.
The best chance of the half came the way of Town on 25 minutes, Liam Henderson released Jack Foalle but the forward saw his shot take a deflection off Keenan Quansah and go over the bar.
On 35 minutes, on-loan forward Ntumba Massanka broke forward with Celtic but again when well placed he could only fire at Lowson.
The home side looked to go into the interval ahead but Johnson bent an effort into the arms of Hughes and also having a header cleared off the line by O’Grady.
Morpeth started the second half on top with Johnson again the main threat as he curled an effort at Hughes.
Three minutes into the second half, Wayne Phillips went on a mazy run but after beating a couple of defenders before his finish was wide of the post and into the side netting.
On the hour, Foalle got into a good position but was only able to shoot at Hughes before Johnson whipped in a low ball across goal which Foalle just couldn’t get a touch on.
The visitors had a glorious chance to take the lead on 74 minutes as a defensive lapse presented Johnson with the ball and Lowson out of his goal but he was caught in two minds and Turner was able to get back and steal the ball.
Morpeth took the lead on 83 minutes and it was deserved for their second half display. Ryan Donaldson was brought down 25yrds from goal and Johnson curled an effort around the wall which found the bottom corner. Hughes will have been disappointed to have not kept it out having got to the ball.
With the Highwaymen thinking they’d secured another three points, Celtic levelled things up. A long ball was flicked on Massanka for Correia who lobbed Lowson from the edge of the penalty area to ensure Stalybridge headed home with a point.
Morpeth are next in action on Saturday when they make the trip to Nottinghamshire to face Basford United.