Romania stay top with 14 points from six matches, one ahead of Northern Ireland and three clear of Hungary, who won 1-0 in Finland, who are second bottom with four, earlier on Saturday.
The hosts should have claimed three points late but an unmarked Kyle Lafferty failed to make a proper connection when the ball fell to him inside the penalty area and Romania's keeper Ciprian Tatarusanu saved with ease.
Manchester United defender Jonny Evans came closest to breaking the deadlock in the first half but his powerful header just before the interval was well saved by Tatarusanu.
Lafferty fluffed another chance midway through the second half as the tackles flew in.
The more technical Romanians did cause some problems and were almost gifted a goal when Gareth McAuley's careless pass sent Gabriel Torje surging towards goal but Evans came to the rescue, deflecting his shot just wide.
Oliver Norwood forced another save from Tatarusanu and Lafferty's late miss meant the game ended all square to keep both sides on course for automatic qualification.
"There's a sense of disappointment because we had the momentum in the second half," Northern Ireland midfielder Steven Davis told Sky Sports. "We couldn't really find that quality in the final third of the pitch.
"Maybe it's a bit of an opportunity missed, but it's still a good point."
Northern Ireland have never qualified for the European Championship and have not played in a tournament finals since the 1986 World Cup in Mexico.
(The story was refiled to correct the last paragraph to say...1986 in Mexico not Spain)
(Reporting by Martyn Herman; editing by Ken Ferris)
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