Jorge Costa's Pacos side came into Friday's game on a dismal run of form, having taken just two points from their final six Primeira Liga fixtures.
Desportivo, meanwhile, finished fourth in the Liga de Honra, and only qualified for the play-offs due to Porto II being ineligible for promotion.
Fernando Valente's men, unlike their visitors, came into the game full of confidence, having tasted defeat only once in their past 11 outings.
That run was extended on Friday as neither side was able to break down their opponents, with defences very much on top in Vila das Aves.
The Primeira Liga outfit will feel confident of preserving their top-flight status after the stalemate, although they will be wary that, ahead of the return leg on Wednesday, they have not won at home since March 23.
Desportivo, meanwhile, have lost just once in their last 11 away matches.
