The Candystrips were convincing 4-0 winners with the goals coming from Patrick McEleney (15th), a penalty from Rory Patterson (25th), Mark Timlin (47) and Bary McNamee (86).
The visiting Welsh side played almost an hour with ten men after their keeper took down Patterson which resulted in the penalty.
Next for Derry is Athlone in the league on Sunday with the Europa second leg next Thursday, 10 July in Wales.
If Derry progress they will face FC Shakhtyor Soligorsk of Belarus in the second round of the qualifiers.
Ramelton's Barry McNamee said getting a result at home in the first leg was vital.