The striker opened her 2020-21 account in the Spanish top-flight as the defending champions claimed their third straight victory.
A Mariona Caldentey’s perfect pass allowed Oshoala to score her first league goal of the season after just five minutes.
Three minutes later, Kheira Hamraoui doubled the lead for Barcelona before Alexia Putellas made it three minutes from half-time.
In the second half, Caldentey was involved in goal again, this time getting on the scoresheet herself for Barca’s fourth of the match before Caroline Graham Hansen made it five for the visitors in the 76th minute.
Oshoala, 26, was in action for 68 minutes and has now scored one goal in three matches this term.
The champions next play Real Betis after the international break.