Sweden forward Fridolina Rolfo put the Germans ahead against the run of the play in the 58th minute.
She fired in from close range as Barca, beaten finalists last year, failed to clear the danger.
Barca had 16 attempts on goal but only once managed to test Wolfsburg goalkeeper Friederike Abt, who saved a header from Oshoala in the first half.
The ball had appeared to deflect off the hand of Wolfsburg defender Kathrin Hendrich, but the Spanish side’s appeals for a penalty kick were ignored.
Oshoala headed narrowly over the bar soon after Rolfo’s goal while Spain internationals Mariona Caldentey and Jennifer Hermoso also missed the target.
Wolfsburg saw the game out to book their place in the final on Aug. 30 against either holders Olympique Lyonnais or Paris St-Germain (PSG), who meet on Wednesday.(Reuters/NAN)