A 36th minute penalty from Rasheedat Ajibade was enough to bring Nigeria their first points in Group D.
The Super Falconets lost their opening match to Germany 1-0 on Monday.
This result moves Nigeria up to second in the table after two games, three points behind leaders Germany.
China are third, level on points with Nigeria, with Haiti bottom - still without a point.
Nigeria's final group game will be against China on Monday.
There are four groups of four with the top two teams progressing to the quarter-final stage.
Ghana's hopes of qualifying to the last eight were dashed with a 4-0 defeat to the Netherlands on Wednesday.