The visitors scored the game’s first points, with a penalty from Tom Harrison.
Pocklington then applied the pressure and scored the first try through Euan Walker to give his side a 7-3 lead.
Both sides were locked together until the 66th minute when a penalty extended the Pocklington lead to 10-3.
The visitors gave themselves a lifeline with a try in the 69th minute.
Harrison kicked the ball over the defence for winger Tom Makin to collect and score in the corner.
Another Pocklington penalty stretched the lead to 13-8 courtesy of a Scarborough mistake at the breakdown.
With just seconds remaining, Matty Jones’ side were, again, penalised at the ruck and took the penalty quickly to score close to the posts. The conversion was successful to give the home side a 20-8 victory.
READ CHARLIE HOPPER'S FULL MATCH REPORT AND SEE ANDY STANDING'S PHOTOS IN THURSDAY'S SCARBOROUGH NEWS