Taking a 5-1 lead into the game, Michael Laudrup rang the changes and one of those switches, Rory Donnelly, missed the first chance of the game as dragged an effort wide.
Donnelly had another chance just before the break, as he raced clean through on goal but chose to take his time to strike the ball, allowing the Ploiesti to get back at him and clear the danger.
After half time, Donnelly again had another golden opportunity as he raced clear on a counter-attack, he played the ball to the back post where his effort was deflected onto the post and the home side managed to clear the danger.
However, the Swans found an equaliser immediately Roland Lamah volleyed in at the back post after latching on to Angel Rangel's cross from the right.
This parity didn't last long as the home side regained the lead in the 87th minute when Guilherme lifted a cross into the middle and found the head of Hamza Younes, who nodded past Tremmel.
Matters got worse for Swansea when Leon Britton was given a second yellow card for refusing to move when Ploiesti were aiming to take a free kick, but Laudrup's side held out for the aggregate win.