Double heartbreak in Cup finals
The Swans were seeking to become the first side to lift the trophy three times, having won it in 2009/10, and repeated the feat a year later, beating Heath in the final.
After a tight first half Ryan Millward powered a header into the top corner from a corner.
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Hide AdDan Molloy sealed the victory with a breakaway goal running onto a through ball from half way as Newport Pagnell looked to get back into the match.
Olney Town too tasted defeat in a cup final as they lost 2-1 to Risborough Rangers in the Intermediate Cup final on Saturday.
Olney took the lead through a Jack Weedon free kick. But a Justin Gordon own goal got Rangers back in it, forcing extra time.
And five minutes from a shoot out, Chris Davies scored the winner giving Olney little time to get back on level terms.