Goals from Dean O'Halloran and Cody Mulhall secured the win for Ireland over the Romanians despite being a man light come the final whistle
Tom Mohan's side finished level on points with Sweden in the group after the Swedes beat the hosts FYR Macedonia 4-0 in the group's other fixture this afternoon.
Ireland's success came despite the dismissal of Dean O'Halloran for two bookable offences seven minutes from time. The two yellow cards came within three minutes of each other.
O'Halloran had broken the deadlock when he found the Romanian net in the 11th minute. Cody Mulhall started a move with a clever pass out wide to Stephen Confrey on the right. The striker's run made space for O'Halloran to burst through and Confrey found O'Halloran with a reverse pass that the Fulham midfielder excellent converted via an upright.
Mulhall increased Ireland's lead in the 56th minute after Dan Cleary had headed across goal following a deep free kick and the Irish then produced a controlled display to hang on for the three points.
"We started really well. It was probably the first game we've started well all week," explained Mohan. "We created numerous chances early on and got a very good goal. That meant Romania had to throw caution to the wind as they needed to win and a draw was good enough for us to progress.
"Romania put us under a lot pressure late in the first half but we scored a good second goal to ease the pressure.
"Dean's red card was harsh considering some challenges that hadn't been punished earlier in the game but with the ten men we defended very well.
"Overall it was a great group effort all week from the staff and the players. The attitude and character the players showed all week was a credit to them.
"It's my first season as manager and obviously I'm delighted to progress to the next stage. There's a great sense of relief but we've a good squad of players and I'd seen them last year when they were well-developed under John Morling.
"I've been very lucky to have worked and learned a lot from John and Sean McCaffrey before that. The staff here have great experience and it's been a group effort. Everybody did their roles from administration to kit-man, analysis - everybody put in a massive effort."
ROMANIA: Fila, Moglan, Bucur (Tudorie 41), Ludusan (Gabor 68), Marin, Puşcaş, Erdei, Torişte, Nedelcearu, Balaure, Dajbog (Haranguş 41).
REPUBLIC OF IRELAND: Peter Burke, Robin Dempsey, Daniel Cleary, Noe Baba, Craig Donnellan, Dean O'Halloran, Cody Mulhall, Jack Byrne (Cian Kavanagh 84), Jake Mulraney (Cory Galvin 58), Bobby Moseley, Stephen Confrey (Eoghan Stokes 48).