The Seasiders raced to an early 10-0 lead thanks to a penalty, try and conversion from fly-half Tom Harrison before winger Matty Young touched down to stretch the lead to 15-0.
Scarborough went off the boil in the second quarter and West Park reduced the arrears to a couple of points at 15-13.
However, a brilliant individual effort by young back row Drew Govier, converted by Harrison, saw the Seasiders grab a 22-13 half-time lead.
A howler by Harrison immediately after the break when he completely missed a cross-field kick saw Leeds run in a converted try to close the gap at 22-20.
An exchange of penalties saw Scarborough lead 25-23 before two late kicks by Harrison clinched an unconvincing 31-23 win.
The Silver Royd men will have to improve considerably if they are to get anything from their game with high-flying Bridlington at Dukes Park next week.
FULL REPORT AND PICTURES BY ANDY STANDING IN THURSDAY’S SCARBOROUGH NEWS