Hessle played some neat football and opened the scoring on 10 minutes as loose marking at a free-kick let them in.
Soon after they doubled their lead with a good move, after a strong run down the right wing the Hessle forward picked out an onrushing midfielder to side-foot home.
Tom MacDonald reduced the arrears midway through the half, curling a superb 25-yard free-kick into the top-corner to give the home side a lift.
Jack Rogers then had a goalbound effort blocked at close range, and this was to prove significant as Hessle restored their two-goal cushion just before half-time.
RETRO SPOTLIGHT: 15 nostalgic Scarborough photos from the Scarborough News sports archives
Commonwealth Games 2022: Scarborough's Chris Turnbull and Team England win bowls mixed para pairs bronze medal
Scarborough Athletic slip to 2-0 defeat at Brackley Town in National League North opener
Elliot Hatton's ton and five-wicket haul helps Flixton to 265-run home win against Cottingham
Ebberston battle back to sink hosts Filey in SBL Premier Division thriller
Playing against the wind and the hill, Scalby found the second half tough, but they stuck to their task.
Despite a deflected goal to make it 4-1, they continued to press forward and were rewarded with another goal, Luke Halliday opening his account for the club with a fine 20 yard finish after Lewis Tadman’s surging run was thwarted by the Hessle keeper.
MacDonald almost snatched another with a late free-kick but the keeper made a smart save to send the Harriers into the semi-finals.
Heslerton Under-15s saw their FA Minor Cup dream come to an end as neighbours Brooklyn won by three goals.
The continually-improving Division Three side came close on several occasions through Morgan Kendrew and Jamie Atkinson but it wasn’t to be for the hosts against the outfit from Division One.
Reece Sleight and Alex Muir impressed along with Heslerton keeper Will Gilbank and the man of the match award went to the Blues defender Robbie Lang.
Heslerton Under-14s snatched an excellent 2-1 win against a high-quality Hamilton outfit.
After an early barrage on the Heslerton goal, Tom Horsley found Jayden Isaac to snatch an early lead for the hosts against the run of play, which he doubled following good work from Dylan Fawcett in midfield.
When Brad Spiller was carried off with a leg injury, stand-in keeper Ben Peckitt produced a spectacular reflex save to send Heslerton in two-up at the break.
It proved to be the crucial moment of the match.
In the second half Hamilton laid siege on the Heslerton goal.
Charlie Richardson tackled himself to a standstill, while Ben Flinton found moments of quality to alleviate the pressure.
The visitors curled in a harshly awarded free-kick with 10 minutes to go, leaving Heslerton to hang on for the final minutes.
Joint men of the match were Horsley and centre-half Ben Robinson, who stood firm to give Heslerton a much-needed three points.
Seamer Under-12s played out an entertaining 1-1 draw away to Brooklyn.
In an end-to-end game Brooklyn took the lead early on only for Seamer to hit back through a Cameron Murray goal.
In the second half chances came and went for both sides, but Seamer came from Malton with a share of the spoils.
Heslerton Under-11s welcomed West Pier Warriors.
Rio Howden opened the scoring before a well worked Pier equaliser.
Pier then took the lead in the second half before Johnson levelled things up late on to leave the sides all square.
Harry Thompson was given the man of the match award.
Game two saw the home team take the lead through strikes from Matthew Moss and Johnson again before Pier got one of their own but the home team hung on for victory.
Man of the match went to Warren Stanton.
Heslerton Under-Eights travelled to Kirkbymoorside.
Game one was fiercely competitive with Reece Wright getting the only goal of the game.
Keane Welburn took the player of the match award.
Game two saw Archie Pilmoor, Welburn and Charlie Driver on the scoresheet for Heslerton.
Wright claimed the player of the match award.