And club-mates Abi and Jess Smee made it a fine day for Hessle by helping Hymers College to victory in the team event.
Former Yorkshire Under-14 champion Allenby shot a one-over-par 73 to win by four shots, his round opening with six straight pars.
The 16-year-old, who plays off two and has represented England at regional level, then birdied the seventh after playing his 100-yard approach shot to within five feet of the cup.
Five more pars followed for the Yorkshire Under-18s player before he returned to level against the card with a dropped shot at the par-3 13th.
Four further pars and a bogey six at the last completed an admirable 73 for the East Riding and Yorkshire Boys player, who last year was selected to represent the East Riding senior team while only 15.
Hymers qualified for next month's county final, to be held at Low Laithes GC, with scores of 77 from both three-handicapper Abi Smee and her five-handicapper sister Jessica, and a 78 from school team-mate Alex Limb, who also plays off five and is a member of Brough GC.
Jessica is this year’s junior captain at Hessle having taken over from Abi, who held the post last year.
Two days after playing at Low Laithes, Hymers will head for St Andrews for the Independent Schools' Golf Association national match play final.
Hymers, who play their team home matches at Hessle, qualified for the event - again through the efforts of the Smee sisters and Limb - where they will play 36 holes over the Torrance Course, at St Andrews Bay, and St Andrews' Eden course.
After a walkover in round one of qualifying, Hymers defeated Sedbergh 3-0 and were then engaged in a nailbiting climax to the area final against Worksop.
Playing at their opponents' home course, College Pines, the encounter stood at 1-1 and the final match, involving Abi Smee, was level through 18 holes.
Abi showed great composure and skill in the sudden-death play-off to birdie the first extra hole and seal progress to St Andrews.