There was no dream start to life in the Welsh Premier for Llangefni, as Adie Jones' side lost out to Jim Hackett's remodelled Nomads.
But Connah's Quay were forced to come from behind before claiming the spoils, courtesy of a late penalty from Chris Williams.
Kevin Lloyd had put Cefni in front after 22 minutes, seizing on a miss by Nomads' keeper Paul Pritchard, but they failed to retain the advantage at the break as John McAllister steered a header past stranded keeper Farai Jackson to level matters on 40 minutes.
Town then squandered a chance to regain the lead when Dylan Owen's penalty was saved by Pritchard and paid the price 12 minutes from time when Adrian Jones fouled Tom Baker and "Bungle" Williams made no mistake with his penalty chance.
"We had four obvious scoring situations, including a penalty and a one-on-one, but failed with each and yet Connah's Quay had only three chances but scored twice," bemoaned Cefni boss Jones.
Stats and report courtesy of welsh-premier.com