The hosts shaded the first half and went closest to breaking the deadlock when Alexandru Chipciu volleyed against the underside of the bar.
They eventually broke Northern Ireland’s stubborn resistance in the 74th minute when Papp lashed home from inside the box.
The defender then headed in a second five minutes later to make sure of the points and lift Romania to the top of Group F.
Northern Ireland slip down to second in the group but have a two-point cushion over Hungary, who beat Finland 1-0.
While the result is a disappointment for Michael O’Neill’s men, it is far from a disaster, especially as they have taken six points from three tricky away matches.
They were also forced into three changes as injured trio Steven Davis, Shane Ferguson and Jamie Ward were replaced by Ryan McGivern, Chris Brunt and Niall McGinn.
McGivern in particular was under plenty of pressure in the first half as Northern Ireland sat back and allowed the hosts to control much of the ball.
However, only on a couple occasions did Romania breach Northern Ireland’s solid defensive line. They came closest to breaking the deadlock in the 18th minute when Chipciu volleyed against the bar and then headed the rebound at Carroll.
Bogdan Stancu also went close when he failed to make contact from a few yards out after a fantastic driving run into the box from Lucian Sanmartean, Romania’s standout player of the first half.
Northern Ireland’s best openings came on the counter attack as Chris Brunt shot narrowly wide from an acute angle and then Lafferty hit a tame effort at the keeper late in the half.
Romania continued to dominate possession after the break and Carroll did well to block a shot by Razvan Rat after a clever pass by substitute Claudiu Keseru.
It looked as though the visitors would hold out until Romania finally broke through in the 75th minute when a cross from Rat fell to Papp and he fired home from 10 yards out.
The defender then put the result beyond doubt five minutes later when he headed in at the back post after a fantastic cross from Sanmartean.
Northern Ireland saw more of the ball in the closing stages as they pressed for a goal but they were unable to trouble keeper Ciprian Tatarusanu.