Still basking in the ecstasy of their 3-1 away triumph over Madrid last time out, Eibar began the game on an impressive note and had the first chance at goal but Cata Coll saved a threatening free-kick.
That proved to be a reality check for the reigning European champions who soon took control of ball possession.
They took the lead in the 19th minute as Swiss star Ana Crnogorcevic headed a Lieke Martens cross past goalkeeper Noelia Garcia.
Five minutes later, Oshoala doubled the advantage for the visiting side after tucking the ball inside an empty net following a goalmouth scramble in Eibar’s penalty area.
Although, credit must be given to Crnogorcevic for troubling the hosts’ backline.
In the goal-laden first half, Jonatan Giraldez’s side went three goals up six minutes before the half-time break courtesy of Jenni Hermoso who was teed up by Dutch star Maertens.
Barca came close to scoring more goals before the break but they wasted those opportunities.
While Maria Leon sent one over the crossbar, Claudia Pina’s powerful effort was saved by goalkeeper Noelia Garcia.
Many would have predicted a harvest of goals in the second half but Eibar put up a solid defensive display to keep the scoreline decent.
After featuring for 59 minutes, four-time African Women’s Player of the Year Oshoala was subbed off for Norwegian midfielder Ingrid Engen.
On the other side, Zambia international Racheal Kundananji was introduced for Ana de Teresa a minute before the hour mark.
Whereas, Equatorial Guinea’s Ruth Alvarez and South Africa’s Noko Matlou were not listed for action.
The Blaugranes remain at the summit of the Spanish top flight with 27 points garnered from their first nine league matches played so far.
Unbeaten in their last 12 matches in all competitions, Barcelona welcome Levante to the Estadi Johan Cruyff in their next league outing on November 13.
Three days earlier, they will square up against German side Hoffenheim in a Champions League encounter.