The visitors made the ideal start and scored a third-minute unconverted try.
Three minutes later it was all-square at 5-5 thanks to a Matty Young try, but then in the 11th minute Scarborough skipper Matty Jones was yellow-carded.
In the 21st minute, Jordan Wakeham went over from close-range and the conversion followed to put the home side ahead for the first time at 12-5.
A solo effort from Tom Ratcliffe then stretched the home side's lead to 19-5 in the 29th minute.
Morley refused to submit thought and reduced the deficit to 19-12 a minute before the interval with an unconverted try.
Four minutes after the restart, Aaron Wilson's try secured the bonus point for Scarborough, and the conversion put the Silver Royd men 24-12 up.
Sam Dawson's converted try secured the win for Scarborough in the 65th minute, the hosts leading 31-12.
Two quick tries from James Perrett and Manning Smith made it 43-12 to Scarborough, Perrett's efffort being converted by Ratcliffe.
The visitors scored another try but a Wakeham interception try, converted again by Ratcliffe, made the final score 50-17.
READ THE FULL MATCH REPORT IN THURSDAY'S SCARBOROUGH NEWS