Brazil led 3-2 and looked to be heading for a victory when the Netherlands equalized.
Wolfsburg player Dominique Janssen elegantly screwed in a free kick from long range with only ten minutes left.
By then, Brazil had in turn come back from a 1-2 defeat by a goal on a penalty by Marta and then a lead goal by Ludmila within four minutes with barely half an hour left.
The Netherlands' big star Vivanne Miedema scored two goals for her team.
The match was the big meeting in the group and the result means that Brazil and the Netherlands have four points each.
China and Zambia played 4-4 in Saturday's second match in that group.
In the next match, Brazil will face Zambia, who was beaten by the Netherlands 10-3 in the premiere, while Brazil beat China 5-0.
The team that scores the most goals on the two worse teams in the group finishes first and gets an easier draw in the quarterfinals.
Right now, the Netherlands have two plus goals to spare.