The Seasiders fell 3-0 behind when Heath full-back Ezra Hinchliffe stroked over an early penalty.
However the visitors’ advantage was short lived and Scarborough fly-half Tom Harrison evened things up with a ninth-minute penalty.
The visiting pack had the upper hand for most of the first half and Scarborough lost the services of hooker Ethynne Terblanche after one particularly bruising ruck .
However it takes more than a bit of ‘grunt’ up front to win a rugby match and Scarborough took a deserved lead on the half hour when lock Aaron Wilson finished off a powerful drive and Harrison kicked the touchline conversion for a 10-3 lead.
The second half continued with a real arm-wrestle and Scarborough had a lot of defending to do.
However Heath never really have the edge to convert their pressure into points and tries from skipper Matty Jones and prop Nino Cutino, both converted by Harrison put the issue beyond doubt.
Next week Scarborough are on the road at Hullensians whose 52-12 defeat at bottom club Acklam was the surprise of the season so far.