Northern Ireland had early chances in Romania as captain Simone Magill fired over the top after a teasing cross by Maxwell.
Defender Rebecca Holloway should have opened the scoring but fired over after a corner fell to her in the six-yard box, and Ellie Mason headed wide from Lauren Wade's delivery.
Romania, ranked five places below NI in 49th, had a penalty appeal waved away after Sefania Vatafu fell in the area under a challenge from Rachel Dugdale, though replays showed there was minimal contact, if any, from the Blackburn Rovers defender.
The highlight of the game came courtesy of Maxwell, who fired home a superb opener.
Brenna McPartlan showed good awareness to cut a ball out of the Romanian defence, and she found Megan Bell in space.
Bell raced forward and spotted Maxwell in space, and the Burnley winger took one touch and arrowed the ball into the far corner.
While Maxwell's goal was a moment of magic, five minutes later the Northern Ireland defence had a moment to forget.
A long ball was fired forward by Maria Ficzay which evaded both Mason and Dugdale, who had both left the clearance to each other.
That allowed Ciolacu all the time and space required to poke the ball past Jackie Burns to level the game.
Oxtoby's side had conceded two goals in quick succession in both their previous Nations League matches, and it nearly happened for the third game in a row when Burns passed the ball straight to Cristina Carp, who could only send her effort wide from 20 yards when she had the whole goal to aim at.