Conwy took the lead early on 10 minutes through Jordan Wells with a good header from a corner.
Conwy's second came after 62 minutes when Ricky Evans scored with a close range volley.
Luke Gethin then gave Llanfair hope. A Richard Ainsley cross found Andrew Hughes whose header was well saved and Luke Gethin put in the rebound.
However, Conwy then sealed the 3 points late on through Toby Jones.
Flint Town United at home next week.