Tiaan Loots and Ross Davies scored the North Walians' tries, with Jacob Botica kicking five points.
Lewis Williams crossed for Pontypridd while teenager Ben Jones landed two penalties in a tense final.
Earlier Penallta won the Plate final on a try-count and Shane Williams' Amman United took the Bowl.
The two sets of Cup final supporters created a noisy atmosphere with Pontypridd fans enjoying their 12th final while the North Wales newcomers were tasting the experience for the first time.
South African centre Loots' try from Botica's inside pass helped put RGC ten points up in the second quarter.
But Ponty pulled back to 10-8 at the interval as wing Lewis Williams made the most of an opportunist quick throw-in, with opposite number Rhys Williams in the sin-bin.
Jones nudged them ahead with his second penalty on 45 minutes, after veteran player-coach Phil John was harshly yellow-carded for a  ruck offence.
But fellow prop Davies was awarded RGC's second try by the TMO eight minutes later, in a pile of bodies on the line.
That proved enough for the team coached by former Wales wing Mark Jones to hold on through a tense scoreless final quarter, and take their first top-flight club honours.
Botica, son of former All-Black Frano, was named man of the match.
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The second-tier Plate trophy went to Penallta on a 2-1 try-count after a 16-16 draw with battling Ystalyfera, who had flanker Jesse Patton sent off after 20 minutes.
Maxfield George's 79th-minute corner try for the Pitmen was decisive after Joe Scrivens' two early penalties and a Corey Tucker try.
Steffan Castle kicked 11 points for their Swansea Valley opponents, who were also awarded a penalty try.
Former Wales wing Shane Williams scored the opening try and had a hand in three others as Amman United beat Caerphilly 43-31 in the third-tier Bowl, with scrum-half Joel Foster kicking 23 points.
RGC 1404 battled to a 15-11 victory over Pontypridd in the National Cup final to lift the trophy for the first time at the Principality Stadium.