The away side established an early 2-0 lead, but Heslerton Under-12s' spirit emerged – typified by man of the match Hayden Williamson – and they battled admirably.
Heslerton created chances themselves, before Kirkbymoorside extended their lead before half-time.
The second half was very similar, but an early penalty scored by Kirkbymoorside made a comeback unlikely.
Both sides created chances, but the visitors pulled away to run out 6-0 winners.
Goldsborough Under-16s made up for their loss the previous week to their visitors by running out comfortable 5-1 winners on a cold, wet afternoon against Scalby.
Scalby equalised through a close-range effort from Callum Pllu, and although they had chances to take the lead they were unable to stop the hosts from pressing home a comfortable second-half advantage.
Keeper Max Tadman was star man for the Otters, producing a string of fine saves to keep the score respectable.
Goldsborough’s win kept them in second spot, closing the gap to leaders Flixton to five points with a game in hand on the pacesetters.
Elsewhere on a weekend fixture schedule hit by the wet weather, Hunmanby Juniors Under-14s inflicted an eighth straight defeat on Kirkbymoorside, beating them 6-3.
Heslerton Under-Eights took on Holt Filey FC.
Freddie Lunn played very well in goal in order to receive the man of the match award, while Alfie Rouph and Harley Bott combined excellently in defence.
After starting in goal, Joey Palmer came out to join Owen Ellis in midfield and there was some tough tackling from both players.
Aaron Walton was enthusiastic and Ryan Cooper continued to support the team by defending from the front.