Simon Smith's Scarborough side raced into an early 8-0 lead via a Matty Young try and Tom Ratcliffe's penalty.
Malton hit back for 8-5, but Scarborough were soon back in command, Aaron Wilson crashing over and Ratcliffe converting for a 15-5 advantage.
Superb work from Tom Hicks then helped Jonty Holloway to extend the lead, before Wilson's second handed the hosts a 27-5 lead.
Malton had the last say of the first half, with the score 27-12 at the interval.
A superb solo effort from James Perrett soon made it 34-12 after the break, but Malton again rallied and two tries narrowed the Scarborough lead to 34-26.
Any Scarborough nerves were settled thanks to Joe Marshall's superb diving effort, which was converted by Ratcliffe to wrap up an impressive 41-26 win.