Opening the innings, Butcher - who has played for the club’s under-17s this summer - hit 63 off 85 balls, his maiden SPL half-century, as Hambledon piled up 265-8 in their final fixture at Basingstoke & North Hants 2nds.
Henry Glanfield also smacked 63 - in his case with five fours and five sixes off just 41 deliveries - in sharing a second wicket stand of 106 with Butcher after Hambledon had chosen to bat.
Opener Dan McGovern (36) and Chris Pratt (40) completed a strong effort by the top five at May’s Bounty.
Oliver then bagged an SPL-best 5-29 off 4.4 overs as Basingstoke were bowled out for 135 to lose by 130 runs.
Another teenager, Shahryar Khan, had sparked one collapse - taking 3-28 as the hosts slumped from 46-1 to 56-4, with Neil Shelar, Alex Yeates and Cian Smith all dismissed without scoring.
Oliver later instigated another collapse - three of his wickets coming with the Stoke score stranded on 100.
It was Hambledon’s 10th win in 11 matches, and they ended with a points-per-game average of 20.36 - easily the highest across the four SPL divisions.
Purbrook, who endured a shocking start to the campaign, avoided relegation to the Hampshire League with a five-wicket victory over Gosport Borough.
They dismissed Borough for 99 before winning on 103-5 in the 34th over.
But those bare stats disguise the fact that Purbrook were given a huge scare before being able to celebrate survival.
With Ollie Creal bagging four wickets, the hosts lurched from 16-1 to 20-5.
They were rescued by Brad Mengham and James Barber, who added an unbroken 83 for the sixth wicket.
Mengham dominated the partnership, hitting 10 fours in his undefeated 64. Barber, who hit four of the 52 balls he faced to the boundary to end on 16 not out, played a fine supporting role as Purbrook finished less than a point above relegated Hythe & Dibden on a PPG basis.
Tom Amis (2-14) reduced Gosport to 9-3 after they had elected to bat with Mengham (2-4), James Gurner (2-9) and Martin Lee (2-25) also among the wickets.
Mark Toogood (30) top scored for Borough, whose last three wickets tumbled with the score on 99.
Portsmouth & Southsea would have finished third (only the top two go up) had they beaten Langley Manor; as it was, they lost by 42 runs and so Manor leapt above them.
Manor were 29-3 before Steve Harris (88 at a run-a-ball, including five sixes) and wicket-keeper James Purnell (84 not out) shared a 162-run stand to help their side post 219-4.
Shaun Briggs (58) and Matt Benfield (35) laid good foundations with an opening stand of 74 for P & S. But only Chris Bollom (24) got above 11 after that as the hosts were dismissed for 177.