The result means Lluis Cortes' ladies advanced with a 2-0 aggregate win on Sunday, and has become the first Spanish club to reach the final of the European women's club competition.
The Blaugrana went into the match in Barcelona needing at least a draw after gaining a 1-0 first-leg advantage, and they claimed a back-to-back win to book a final berth.
The Nigerian, who made her second outing in the competition, replaced Toni Duggan in the 71st minute to ensure 10-player Cortes' side claimed a win through Mariona's strike from the spot.
It was the 24-year-old's ninth appearance in all competitions for Barcelona since joining in February and she has scored seven goals in six league games this season.
Before their trip to Hungary, Barcelona will be looking to claim the Liga Iberdrola title with a final day win at Tenerife, hoping leaders Atletico slip at Real Sociedad on Saturday.