The home side raced into a 6-0 lead after a series of back to back penalties, with Jordan Wakeham slotting them both over the posts.
The visitors scored the first unconverted try of the game when a defensive mistake presenting Will Kinder with the opportunity to score in the corner.
Morley then took the lead with a penalty in the 27th minute, but Scarborough hit back with another penalty to retake the lead.
On the stroke of half-time, Morley took the lead after winning a penalty in front of the posts to leave them leading 11-9.
The Maroons started the second-half in the perfect fashion with another unconverted try through Noah Hawkins.
The lead was stretched even further in the 57th minute, when Nick Green capitalised on home errors to score in the corner for a 21-9 lead.
Man of the match Billy Parker gave his side a glimmer of hope with a converted try in the 66th minute.
Both sides then exchanged penalties to leave the visitors leading 24-19. With just seconds remaining, the returning Domett scored a converted try to give his side the victory.
Matty Jones’ side are on the road next weekend at Pocklington.