Stalybridge got a well-deserved point in the closing minutes of a game which they dominated for most of the time.
The Conference new-boys confidence never looked back after their man-of-the-match Richard Peacock saw his 18-yard effort strike the post in the second minute after bursting forward to latch onto an un-cleared cross. Andy Woods was then on hand to deny the in-form midfielder in the 13th minute.
Scarborough, who secured their fourth draw of the season, showed none of their form from Saturday at Woking when they enjoyed their first win of the season. They repeatedly failed in front of goal and their lacklustre showing in midfield brought protest from the sidelines.
But the Seasiders had their chances with Steve Brodie masterminding some good moves, only to see them wasted with no one on the spot to finish them off.
Jason Blunt drove a well-placed corner into a crowded goalmouth which Celtic desperately cleared, then a minute later Brodie slipped a neat pass to Darryn Stamp who volleyed the ball inches wide from the edge of the box.
Brodie and Peacock continued to impress at each end but Celtic repeatedly had the upper hand while Scarborough lacked presence at the front.
A dressing room rocket from Scarborough manager Neil Thompson at the break saw an improved showing in the second half, despite the change of Ward for Perkins at right back.
Chris Short broke through and forced Celtic keeper Gary Ingham to produce an excellent dive, full-length, to save. Ingham was again tested with a fine volley from Peter Fitzsimmons.
Brodie beat three defenders on the run then sliced the ball inches wide of the near post.
Ged Courtney slipped a neat ball to Peacock who hit the woodwork with a shot on the run in the 65th minute and two minutes later Peacock had a good chance intercepted by Gareth Stoker.
Scarborough broke the deadlock in the 77th minute when Stoker crossed the ball into the box but it failed to be cleared and Brodie shot on the turn from 12 yards.
Two minutes later Brodie raced down the left and crossed to Blunt who shot wide.
Celtic's equaliser came in the 82nd minute when Gerard Courtney seized his chance after a defensive blunder by the home side to score from eighteen yards.
The result was a double blow for Scarborough who saw their crowd dropped to 867 - the lowest so far this season.
Manager Thompson said he was disappointed that Scarborough had not maintained their form from Saturday's 2-1 victory at Woking despite playing an unchanged side. "Celtic played well and we knew it was not going to be an easy game," he said.
Stalybridge Celtic boss Paul Futcher was disappointed with the draw, and felt his team should have won.
"Although it looks a good result on paper it is a game we should have won," he said. "They didn't play well in the first half and the game was there for the taking but we didn't get going. And then when they scored I thought 'how can we lose this' but we showed a lot of character and bounced back to equalise."
However, two 1-1 results in succession has delighted the Stalybridge boss who is pleased that the players haven't allowed the 4-1 drubbing at Boston to affect them.
Futcher added: "I changed the system to three at the back and they've responded well from the 4-1 defeat at Boston. I'm not rigid about systems in fact I'm flexible but players should be able to adapt - its not asking too much."
The game only saw two cards, both yellow, and one for each team. Blunt received one for a foul on the half hour, and Bushell the other for the foul which led to the Scarborough goal. There was very little to separate the two teams. Scarborough had fourteen goal attempts, with seven on target, and one striking the woodwork. Stalybridge on the other hand had nine shots, with five on target and two off the post. Stalybridge edged the corners stakes, with nine over Scarborough's eight, and both committed nine fouls. Sports.com's rating system marked Scarborough as 71%, and Stalybridge as 74%.