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It was a bright start from the home side, with Nicolae Stanciu and Adrian Popa misfiring with early efforts and failing to test Iker Casillas, who equalled the European record for international caps by making his 166th Roja appearance.
Gerard Pique was the only Spain player to keep his place from Thursday night's 1-1 draw in Italy and the Barcelona man went close to the opening goal with a header that was tipped over by Ciprian Tatarusanu.
The Fiorentina keeper then denied Pedro before Casillas was called upon at the other end to keep out Stanciu's firm effort.
No goals at the break, but the deadlock was almost broken shortly after the resumption as Pique again stung the palms of Tatarusanu from a corner.
In the closing stages of the match it was Spain doing more of the pressing, but Vicente del Bosque's side could not find a winner as Romania ensured that their record of having not lost since June 2014 went on.