The 16-year-old trailed the Renaissance Club’s Dominic McGlinchey with two holes to play in the title decider before winning the short 17th with a par then taking the last as well with birdie-3 after driving the green.
Earlier, Royal High School pupil Johnston had birdied the first, fourth and fifth, with McGlinchey matching him at the first and fifth.
Johnston then won the sixth and seventh with pars before his opponent fought back with birdies at the eighth, tenth and 11th to square matters.
McGlinchey got his nose in front for the first time with a birdie at the 15th before Johnston dug deep to turn the tide back his way.
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His success came two years after clubmate Archie Finnie also got his hands on the Speirs Trophy.
“When he reads down the trophy and sees Graham Ewart as a past winner, he realises how special it is,” said dad Stuart, who is heavily involved in the running of the Stephen Gallacher Foundation.
“Graham helped the SGF when we first started and was responsible for teaching Jake the etiquette and rules he still follows when he was about eight-years-old.”
Referring to the new champion’s late grandad, who was on the Dispatch Trophy committee for a number of years, he added: “Auld Bobby will be toasting him with a whisky!”
McGlinchey beat leading qualifier Rory McClafferty (Linlithgow) 3&2 in the semi-finals, where Johnston was a 4&3 winner over Swanston’s Struan Reinink.