The Dons started the game well and had a couple of chances without seriously threatening the home goal.
Haroldeans showed greater urgency at the start of the second half and they broke the deadlock after 50 minutes when Max Barnett slotted home from a corner.
Maxim Green doubled the lead five minutes later as the Dons started to lose their way.
Sean Cooper capped a man-of-the-match performance with the third goal – a stunning solo effort – and it was left to substitute Jack Bookey to complete the scoring from 18 yards and set up a final against HMH on May 19.
Haroldeans’ assistant-manager Fraser Saville said: "We’ve done well in the competition for the past few season but I always wanted us to be able to compete at the highest level in Jewish football and I think we have proved that now.
“It has always been personal ambition of mine that we win the Morrison and I do think we have our chances. We know HMH are a very good side and have been playing together for a long time but I am sure it will be an interesting game.
“We have had a good season in our first year in non Jewish football, and still have two league games left to play and could possibly just miss out on promotion and like Liverpool, could end up winning nothing at all."
Dons boss Brandon Hamme expressed pride after the second division team suffered cup semi-final heartache for the second time. “To reach this stage was incredible achievement in itself, and they gave it everything on Sunday,” he said.
“We had to contend with some absentees once again, but our players filled in superbly. We defended incredibly well during the first half but the high intensity pressing took its toll in the second half as we began to tire and conceded a flurry of goals.”
Hamme praised goalkeeper Oli Burchell for a “truly superb” performance. He went on to say: “Speaking of superb, that’s what Haroldeans were today, a real proper football team which even as the opposition manager was a pleasure to watch. “I would say that they are the best team we have faced as a club and we wish them all the best in the final.
“We now, we move on and try to solidify fourth place in Division Two with two wins from our last two games needed. I said before the turn of the year that we were severely underachieving and that’s proven to be true with our performances in the cup and in the league this year. In December, I set the boys the target of finishing fourth, so if we were to finish the job it would a real sign of the improvement we have made along with the two semi-finals we have made.
“We can look back at this season as a success if we manage to secure fourth place."