Romania struggled to convert their dominance into goals in the first half as they wasted a couple of chances with veteran Lucian Sanmartean again pulling the strings in midfield.
But right back Papp lashed an unstoppable left-foot shot into the top corner for his second international goal after the visitors failed to clear a cross from Romania captain Razvan Rat in the 74th minute.
Five minutes later, Papp gave Irish keeper Roy Carroll no chance with a brilliant header following a precise cross from Sanmartean.
Unbeaten Romania top the standings with 10 points from four matches, followed by Northern Ireland, who arrived in Bucharest with a maximum nine points from three games.
“I congratulate the entire team and I am happy with what happened today,” said Romania coach Anghel Iordanescu. “The most important thing is that we won
“We tried to play offensively, we had some delicate moments but we managed to overcome them.”
Iordanescu, who returned last month for a third spell as Romania coach, stuck to predecessor Victor Piturca’s favoured 4-2-3-1 system, with Bogdan Stancu as a lone striker in the absence of the injured Bogdan Marica and Raul Rusescu.
Northern Ireland’s Michael O’Neill made three changes from the side that beat Greece 2-0 in Athens last month, with Niall McGinn and Chris Brunt replacing Jamie Ward and Steven Taylor in midfield and Ryan McGivern coming at left back for the injured Shane Ferguson.
Romania’s 25-year-old birthday boy Vlad Chiriches, charged with the task of keeping in-form Kyle Lafferty under wraps, tested Carroll with an amazing overhead kick after Chris Baird failed to properly clear the ball.
The visitors responded with a speedy counter attack and Brunt fired a left-foot shot just wide but they rode their luck when the home side failed to take two excellent chances.
Alexandru Chipciu hit the bar from Cristian Tanase’s left-wing cross before heading straight into Carroll’s arms from the rebound.
Just after the half-hour mark, Sanmarten drove into the box on a brilliant solo run but, with only Carroll to beat, he unselfishly squared the ball to Stancu who fell over, allowing the Irish defence to clear.
Claudiu Keseru, who replaced the ineffective Stancu at halftime, played an excellent ball through to Rat but the home captain failed to beat Carroll in a one-on-one.
Romania then had a penalty appeal waved away after Sanmartean was brought down by Ryan McGivern, who had made a vital interception to deny Gabriel Torje a few minutes earlier.
Northern Ireland’s fairytale start to their campaign finally came to an end when Papp netted twice in quick succession, triggering a deafening roar from the Romania fans.
“Romania are a very strong team – the strongest in the group and there’s no doubt the best team won,” Northern Ireland coach O’Neill said.
“We now have two home games to look forward to and have nine points from four matches, three of which were away to the hardest teams in the group.”
Romania welcome the Faroe Islands – who shocked Greece 1-0 in Athens on Friday — in their next qualifier on March 29 while Northern Ireland, who have failed to reach a major tournament since the 1986 World Cup, host Finland on the same day.
(Reporting by Angel Krasimirov; Editing by Ken Ferris)