Ten-man Llangefni held on for the three points which put them top of Ardal North West with a five-game unbeaten record.
Cefni took a ninth-minute lead when Jack Smith applied a good finish.
On 19 minutes referee Martin Trigg showed a straight red to Llangefni’s Dafydd Jones for what was considered a dangerous tackle.
It remained 1-0 up to half time and the game’s lack of a second goal continued long into the second period.
That all-important goal came Town’s way when Matty Jones made it 2-0 in the 82nd minute.
Four minutes from time, Steffan Davies pulled one back for Bethesda, but the islanders held on to win, having played more than 70 minutes a man down.
This was a fourth defeat in five matches for Athletic, who look to have a squad good enough to start climbing the table soon.
Morgan Jones was a four-goal hero for a Llannefydd side which climbed out of the bottom three after a first league win of the campaign.
Signed from Caer Clwyd in the summer, Jones found the net on 10, 11 and 31 minutes to complete a first-half hat-trick before adding a fourth after 86.
Steffan Williams also struck for Gwyndaf Pritchard’s men to make it 4-0 at half time.
Sam Jones added a fifth on 62 minutes before George Davies pulled one back for Saltney.
An impressive first league success of the season for Dolgellau, with Paul Lewis and Wiliam Gruffydd on target in the opening half before Gerwyn Williams made it three early in the second stanza.
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