Hungary last beat their arch-rivals in 1981 and could not do it this time either in a bad-tempered match with few chances.
The draw saw Romania slip to second place with 15 points from seven games, a point behind Northern Ireland who won 3-1 away to the Faroe Islands. Hungary are third on 12 points.
Hungary's Adam Szalai came closest to scoring for the hosts but the striker's fierce volley from 25 metres was parried by Ciprian Tatarusanu in the 36th minute.
Romania's best chance came in the 78th when Gabor Kiraly made a fine save to keep out Gabriel Torje's left-foot strike.
"It was a difficult game after a difficult week. We had injuries and we had to substitute central defender Roland Juhasz after only 20 minutes. All in all, we have to be happy with a draw," Hungary's German coach Bernd Storck said.
It was his first game in charge after he replaced Pal Dardai, who is now Hertha Berlin manager, in July.
Hungary coach Anghel Iordanescu told reporters: "It was a good game for us, especially in the first half when we had the lion's share of possession and played well. The second 45 minutes was evenly balanced, so we could not attack as much as we planned and had to be satisfied with only one point," .
Iordanescu played the last time Hungary beat Romania with a 1-0 triumph in a World Cup qualifier, also in the Hungarian capital. Their subsequent eight competitive clashes had produced four Romania wins and four draws which now reads five.
Hungary visit Northern Ireland on Monday when Romania host bottom side Greece, who on Friday lost 1-0 at home to Finland, who are fourth with seven points.
(Reporting by Zoltan Fazekas; Editing by Ken Ferris)
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