Rio de Janeiro powerhouses Fluminense were the more dangerous team throughout the Group F game played at the MetLife Stadium in East Rutherford, just outside New York City.
However, Dortmund goalkeeper Gregor Kobel turned a Jhon Arias shot around the post in the first half, before Matheus Martinelli drilled an effort narrowly wide.
Fluminense - captained by 40-year-old former Paris Saint-Germain and Chelsea defender Thiago Silva - were a threat on the break throughout and should have scored at the end of a counter midway into the second half, but Agustin Canobbio shot straight at Kobel.
The Dortmund goalkeeper then produced a fine save low down to deny Everaldo as the match ended in stalemate. Fluminense qualified for the tournament by their triumph in the Copa Libertadores in 2023.