Fourth division champions Snaith started brightly and took the lead in the 12th minute with a goal from Brad Smith, but third division title holders Britannia levelled after 35 minutes when Scott Nicholson scored direct from a corner-kick.
After a miss early in the second half by Britannia’s Oliver Brennan, Snaith broke away and Matt Whitaker netted.
But Britannia were not to be denied.
Sure-shot Nicholson hit his second before top scorer Adam Field was bundled over in the box and Brennan made up for his earlier miss to calmly slot the ball in from a penalty.
Snaith yet again hit back following a long throw that was headed home by Chris Gilmartin to take the tie into extra-time.
Britannia began to get on top and were rewarded when Jordan Willoughby headed in powerfully for the match-winner.
King William claimed their third trophy of the season with a 3-2 win over Marcia Grey in the final of the York Sunday Morning League Cup.
Third division underdogs Marcia took an early lead but King William’s leading scorer Danny Gray struck just before the break when he let a long ball drop over his shoulder and volleyed home powerfully.
Marcia continued to battle and went back in front.
Alex Day collected the ball on the left of the box and unleashed an unstoppable shot into the net.
Gray was again the focal point of the King William attacks. He was upended for Dave Haslem to regain the lead with a penalty.
Marcia were all square moments later following the best move of the game that was started from their own penalty area by Liam Shepherd and finished by Lee Harris.
But King William, unbeaten all season, struck back almost instantly.
Gray went up for an aerial tussle with the Marcia keeper and a defender, who collided with each other.
The ball rolled towards an unguarded net where King William centre-back Ryan O’Reilly poked the ball home to give his side the cup.