Sandro Ramirez tried to open the scoring for the visitors with a long-range effort, but it finished well high of the bar.
However, Barcelona B did manage to edge ahead mid-way through the first half when Javier Espinosa slotted the ball in low from close range.
Nando looked to get the hosts back on level terms at the start of the second half, but fired his shot straight into the hands of the keeper.
Jaen continued to press for an equaliser, but created few chances, and were caught out by the counter-attack from the visitors late on, allowing Jean Mario Dongou to slot home a second.
Oscar Quesada thought that he had got the home side back into the match in the final couple of minutes, but his effort was disallowed for offside.
Dongou was able to grab his second of the day in stoppage time, jumping high in the area to head past the Jaen keeper.