The striker, signed from Burnley last season, was crudely brought down by Javier Arango on 65 minutes. Adam Hamill shaped up to take the free-kick but Fletcher caught the Spaniards by surprise when he floated the ball into the top corner to make it 2-0.
Wolves had opened the scoring a few minutes earlier, when an untidy scramble in the visitors' box saw George Elokobi prod the ball home.
Zaragoza came close to opening the scoring in the first half when Ikechukwu Uche's shot beat keeper Wayne Hennessey, only for Stephen Ward to dramatically clear off the line.
Wolves dominated the second period, with Fletcher hitting the bar from Ronald Zubar's cross, while Matt Jarvis fired into the side netting.